A Switching Approach to Designing Finite-Time Synchronization Controllers of Coupled Neural Networks

Finite-Time Synchronization of Neural Networks With Proportional Delays for RGB-D Image Protection

Since the depth information of images facilitates the analysis of the spatial distance of objects in computer vision applications, it is necessary to protect the image depth information. Thus this article proposes a novel red-green-blue-depth (RGB-D) image protection algorithm, which is implemented with the finite-time synchronization (FTS) of neural networks (NNs) with proportional delays via the quantized intermittent control to derive the system synchronization criterion based on Lyapunov stability theory. The performance of RGB-D image protection depends on the synchronization error of the system by driving the system sequence to encrypt the RGB-D image and responding to the system sequence to decrypt the encrypted image. Subsequently, the validity of the proposed criteria is verified by simulation examples, and the practical application of RGB-D image protection is verified.

Finite-time synchronization for coupled neural networks with time-delay jumping coupling

The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.

Finite-Time Synchronization and H∞ Synchronization for Coupled Neural Networks With Multistate or Multiderivative Couplings

This article investigates the finite-time synchronization (FTS) and H∞ synchronization for two types of coupled neural networks (CNNs), that is, the cases with multistate couplings and with multiderivative couplings. By designing appropriate state feedback controllers and parameter adjustment strategies, some FTS and finite-time H∞ synchronization criteria for CNNs with multistate couplings are derived. In addition, we further consider the FTS and finite-time H∞ synchronization problems for CNNs with multiderivative couplings by utilizing state feedback control approach and selecting suitable parameter adjustment schemes. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed criteria.

Sampling-Based Event-Triggered Exponential Synchronization for Reaction-Diffusion Neural Networks

In this article, the exponential synchronization control issue of reaction-diffusion neural networks (RDNNs) is mainly resolved by the sampling-based event-triggered scheme under Dirichlet boundary conditions. Based on the sampled state information, the event-triggered control protocol is updated only when the triggering condition is met, which effectively reduces the communication burden and saves energy. In addition, the proposed control algorithm is combined with sampled-data control, which can effectively avoid the Zeno phenomenon. By thinking of the proper Lyapunov-Krasovskii functional and using some momentous inequalities, a sufficient condition is obtained for RDNNs to achieve exponential synchronization. Finally, some simulation results are shown to demonstrate the validity of the algorithm.

Passivity and Finite-Time Passivity for Multi-Weighted Fractional-Order Complex Networks With Fixed and Adaptive Couplings

This article presents several new α -passivity and α -finite-time passivity ( α -FTP) concepts for the fractional-order systems with different input and output dimensions, which are distinct from the concepts for integer-order systems and extend the existing passivity and FTP definitions to some extent. On one hand, we not only develop some sufficient conditions for ensuring the α -passivity of the multi-weighted fractional-order complex dynamical networks (MWFOCDNs) with fixed and adaptive couplings, but also discuss the synchronization for the MWFOCDNs based on the α -output-strict passivity ( α -OSP). On the other hand, the α -FTP for the MWFOCDNs with fixed and adaptive couplings are also studied on the basis of the designed state feedback controller, and the relationship between finite-time synchronization (FTS) and α -FTP for the MWFOCDNs is also illustrated. Finally, two numerical examples with simulation results are used to demonstrate the validity of the obtained criteria.

Finite-Time and Fixed-Time Synchronization of Quaternion-Valued Neural Networks With/Without Mixed Delays: An Improved One-Norm Method

In this article, the finite-time synchronization (FTSYN) of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays is studied. Furthermore, the FTSYN and fixed-time synchronization (FIXSYN) of the QVNNs without time delay are investigated. Different from the existing results, which used decomposition techniques, by introducing an improved one-norm, we use a direct analytical method to study the synchronization problems. Incidentally, several properties of one-norm of the quaternion are analyzed, and then, three effective controllers are proposed to synchronize the drive and response QVNNs within a finite time or fixed time. Moreover, efficient criteria are proposed to guarantee that the synchronization of QVNNs with or without mixed time delays can be realized within a finite and fixed time interval, respectively. In addition, the settling times are reckoned. Compared with the existing work, our advantages are mainly reflected in the simpler Lyapunov analytical process and more general activation function. Finally, the validity and practicability of the conclusions are illustrated via four numerical examples.

Finite-Time Synchronization of Markovian Coupled Neural Networks With Delays via Intermittent Quantized Control: Linear Programming Approach

This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

Adaptive Bipartite Time-Varying Output Formation Control for Multiagent Systems on Signed Directed Graphs

The issue of bipartite time-varying formation (BTVF) tracking for linear multiagent systems (MASs) with a leader of unknown input on signed digraphs is investigated. An adaptive nonsmooth protocol is taken in this article that utilizes only the local output feedback information among neighbors and, thus, can avoid employing the eigenvalue information of the Laplacian matrix of the graph. It is proven that if the interaction network of agents containing a spanning tree is structurally balanced, the BTVF tracking can be achieved with a leader of the bounded input via the proposed scheme. This leader-following BTVF includes two time-varying subformations, whose relationship is antagonistic. A convergence analysis of the proposed protocol for MASs is reflected by the Lyapunov method. Finally, the validly numerical simulations are illustrated to show the performance of the proposed schemes.

Delay-Dependent Stability Analysis for Switched Stochastic Networks With Proportional Delay

In this article, the issue of exponential stability (ES) is investigated for a class of switched stochastic neural networks (SSNNs) with proportional delay (PD). The key feature of PD is an unbounded time-varying delay. By considering the comparison principle and combining the extended formula for the variation of parameters, we conquer the difficulty in consideration of PD effects for such networks for the first time, where the subsystems addressed may be stable or unstable. New delay-dependent conditions with respect to the mean-square ES of systems are established by employing the average dwell-time (ADT) technique, stochastic analysis theory, and Lyapunov approach. It is shown that the acquired minimum average dwell time (MADT) is not only relevant to the stable subsystems (SSs) and unstable subsystems (USs) but also dependent on the decay ratio (DR), increasing ratio (IR), as well as PD. Finally, the availability of the derived results under an average dwell-time-switched regulation (ADTSR) is illustrated through two numerical simulation examples.

Finite-Time Output Synchronization of Multiple Weighted Reaction-Diffusion Neural Networks With Adaptive Output Couplings

This article mainly considers the output synchronization (OS) problem of multiple weighted and adaptive output coupled reaction-diffusion neural networks (RDNNs) without and with coupling delays in finite time. Without coupling delays, an adaptive control law and an output feedback controller are, respectively, proposed to ensure that the multiple weighted and output coupled RDNNs are output synchronized and output synchronized in finite time. With coupling delays, an adaptive coupling weights control scheme and a novel feedback controller are put forward to make the multiple weighted RDNNs with output couplings achieve OS in finite time. Moreover, the finite-time OS is considered in the presence of external disturbances. By the Lyapunov approach, several finite-time OS and OS criteria are given. Finally, two simulation examples are presented to justify the effectiveness of the proposed adaptive control laws and controllers.

Finite-/fixed-time synchronization for Cohen-Grossberg neural networks with discontinuous or continuous activations via periodically switching control

This paper is concerned with finite-/fixed-time synchronization for a class of Cohen-Grossberg neural networks with discontinuous or continuous activations and mixed time delays. Based on the finite-time stability theory, Lyapunov stability theory, the concept of Filippov solution and the differential inclusion theory, some useful finite-/fixed-time synchronization sufficient conditions for the considered Cohen-Grossberg neural networks are established by designing two kinds of novel periodically switching controllers. Instead of using uninterrupted high control strength, the periodically switching controller in each period is used with high strength control in one stage and weak strength in the other. It can overcome the effects caused by the uncertainties of Filippov solution induced by discontinuous neuron activation functions and reduce the control cost. Besides, the period switching control rate is closely related to the settling time T. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of the obtained results.

Guaranteed Cost Finite-Time Control of Uncertain Coupled Neural Networks

This article investigates a robust guaranteed cost finite-time control for coupled neural networks with parametric uncertainties. The parameter uncertainties are assumed to be time-varying norm bounded, which appears on the system state and input matrices. The robust guaranteed cost control laws presented in this article include both continuous feedback controllers and intermittent feedback controllers, which were rarely found in the literature. The proposed guaranteed cost finite-time control is designed in terms of a set of linear-matrix inequalities (LMIs) to steer the coupled neural networks to achieve finite-time synchronization with an upper bound of a guaranteed cost function. Furthermore, open-loop optimization problems are formulated to minimize the upper bound of the quadratic cost function and convergence time, it can obtain the optimal guaranteed cost periodically intermittent and continuous feedback control parameters. Finally, the proposed guaranteed cost periodically intermittent and continuous feedback control schemes are verified by simulations.

Finite-Time Output Synchronization and H∞ Output Synchronization of Coupled Neural Networks With Multiple Output Couplings

This article investigates the finite-time output synchronization and H_∞ output synchronization problems for coupled neural networks with multiple output couplings (CNNMOC), respectively. By choosing appropriate state feedback controllers, several finite-time output synchronization and H_∞ output synchronization criteria are proposed for the CNNMOC. Moreover, a coupling-weight adjustment scheme is also developed to guarantee the finite-time output synchronization and H_∞ output synchronization of CNNMOC. Finally, two numerical examples are given to verify the effectiveness of the presented criteria.

Perturbation Analysis for Finite-Time Stability and Stabilization of Probabilistic Boolean Networks

This article analyzes the function perturbation impact on the finite-time stability and stabilization of the probabilistic Boolean networks (PBNs). First, the concept of stability in the distribution of PBNs is divided into two disjoint concepts, that is, finite-time stability with probability one (FTSPO) and asymptotical stability with probability one (ASPO), and a new criterion is proposed for the verification of ASPO. Second, by constructing a parameterized set, it is shown that PBNs subject to function perturbation keep FTSPO if and only if the perturbed point does not belong to the parameterized set, while PBNs become ASPO if and only if the perturbed point belongs to the parameterized set. Third, as an application of perturbed stability analysis, the robust state-feedback stabilization is discussed for probabilistic Boolean control networks (PBCNs) with function perturbation. Finally, the obtained results are applied to a WNT5A network and lac operon in the Escherichia coli, respectively.

Synchronization of Stochastic Complex Dynamical Networks Subject to Consecutive Packet Dropouts

This paper studies the modeling and synchronization problems for stochastic complex dynamical networks subject to consecutive packet dropouts. Different from some existing research results, both probability characteristic and upper bound of consecutive packet dropouts are involved in the proposed approach of controller design. First, an error dynamical network with stochastic and bounded delay is established by step-delay method, where the randomness of the bounded delay can be verified later by the probability theory method. A new modeling method is introduced to reflect the probability characteristic of consecutive packet dropouts. Based on the proposed model, some sufficient conditions are proposed under which the error dynamical network is globally exponentially synchronized in the mean square sense. Subsequently, a probability-distribution-dependent controller design procedure is then proposed. Finally, two numerical examples with simulations are provided to validate the analytical results and demonstrate the less conservatism of the proposed model method.

Finite-/Fixed-Time Synchronization of Delayed Coupled Discontinuous Neural Networks With Unified Control Schemes

In this article, it addresses the problem of finite-/fixed-time synchronization of delayed coupled discontinuous neural networks in the unified framework. To achieve the finite-/fixed-time synchronization and precise estimations of setting time, two novel different kinds of controllers are established, in which one is switching. Then, based on the finite-/fixed-time theorem and Lyapunov function theory, some useful criteria are obtained to select suitable controllers' parameters, which can guarantee error systems converge in the finite time/fixed time with respect to coupled neural networks. Moreover, corresponding estimations of the setting time are also provided. Finally, two numerical examples are introduced to show the effectiveness of the proposed control protocols.

Finite-Time Output Synchronization of Undirected and Directed Coupled Neural Networks With Output Coupling

This article focuses on the finite-time output synchronization problem for undirected and directed coupled neural networks with output coupling (CNNOC). Based on the designed state feedback controllers and some inequality techniques, we present several finite-time output synchronization criteria for these network models. In addition, two kinds of coupling-weight adjustment strategies are also developed to guarantee the finite-time output synchronization of undirected and directed CNNOC. Finally, two numerical examples are also provided to demonstrate the effectiveness of the theoretical results.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

Finite-Time Passivity of Adaptive Coupled Neural Networks With Undirected and Directed Topologies

In this paper, the finite-time passivity (FTP) problem for two classes of coupled neural networks (CNNs) with adaptive coupling weights is discussed. By selecting appropriate adaptive laws and controllers, several FTP conditions are given for CNNs with undirected and directed topologies. Furthermore, some finite-time synchronization conditions are also established by employing the FTP of the CNNs. At last, two numeral examples are used to check the correctness of the obtained criteria.

Finite-Time Synchronization and H∞ Synchronization of Multiweighted Complex Networks With Adaptive State Couplings

In this paper, two kinds of multiweighted and adaptive state coupled complex networks (CNs) with or without coupling delays are presented. First, we develop the appropriate state feedback controller and adaptive law for the sake of guaranteeing that the proposed network models without coupling delays can be finite-timely synchronized and H_∞ synchronized. Furthermore, for the multiweighted CNs with coupling delays and adaptive state couplings, some finite-time synchronization and H_∞ synchronization criteria are presented by choosing the appropriate adaptive law and controllers. Eventually, we give two numerical simulations to verify the validity of the theoretical results.

A Stochastic Sampling Mechanism for Time-Varying Formation of Multiagent Systems With Multiple Leaders and Communication Delays

The time-varying formation problem for multiagent systems (MASs) with stochastic sampling and multiple leaders is studied in this paper, in which communication delays are taken into account. All the agents are divided into the set of the follower group and the set of the leader group. Under the proposed stochastic sampling mechanism for time-varying formation of the MASs with communication delays, the followers are driven to achieve time-varying formation where the center of the formation is the convex combination of the states of the leaders. In the theoretical analysis, sufficient conditions for the MASs achieving time-varying formation in mean square under stochastic sampling with multiple leaders and communication delays are derived. Moreover, some corollaries are also given in this paper. Finally, the theoretical analysis is verified by a given simulation example.

Region Stabilization of Switched Neural Networks With Multiple Modes and Multiple Equilibria: A Pole Assignment Method

This article investigates region stabilization issue of switched neural networks (SNNs) with multiple modes (MMs) and multiple equilibria (ME) via a pole assignment method. In such an SNN, every neuron is observed with more than one mode and unstable equilibrium point. First, SNNs with MMs and ME are modeled in terms of switched systems with unstable subsystems and ME. Second, a necessary and sufficient condition and a sufficient condition are, respectively, proposed for arbitrary switching paths pole assignment and arbitrary periodic/quasi-periodic switching paths (PSPs/QSPs) asymptotically region stabilizing pole assignment of switched linear time-invariant (LTI) systems with ME. It is shown that to stabilize a switched LTI system, some/all poles of all/some linear subsystems can be assigned to suitable locations of the right-half side of the complex plane. Third, based on the obtained pole assignment results, an asymptotical-region-stabilizing-control law observed as distributed state feedback controllers of MMs, asymptotical-region-stabilizing PSPs/QSPs, and a corresponding algorithm are all designed for asymptotical region stabilization of switched linear/nonlinear neural networks with MMs and ME. Finally, a numeral example is given to illustrate the effectiveness and practicality of the new results.

Finite-Time Passivity and Synchronization of Coupled Reaction-Diffusion Neural Networks With Multiple Weights

In this paper, two multiple weighted coupled reaction-diffusion neural networks (CRDNNs) with and without coupling delays are introduced. On the one hand, some finite-time passivity (FTP) concepts are proposed for the spatially and temporally system with different dimensions of output and input. By choosing appropriate Lyapunov functionals and controllers, several sufficient conditions are presented to ensure the FTP of these CRDNNs. On the other hand, the finite-time synchronization (FTS) problem is also discussed for the multiple weighted CRDNNs with and without coupling delays, respectively. Finally, two numeral examples with simulation results are provided to verify the effectiveness of the obtained FTP and FTS criteria.

Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach

Based on the graph theory and stability theory of dynamical system, this paper studies the stability of the trivial solution of a coupled fractional-order system. Some sufficient conditions are obtained to guarantee the global stability of the trivial solution. Finally, a comparison between fractional-order system and integer-order system ends the paper.

Passivity and Synchronization of Coupled Uncertain Reaction-Diffusion Neural Networks With Multiple Time Delays

This paper presents a complex network model consisting of N uncertain reaction-diffusion neural networks with multiple time delays. We analyze the passivity and synchronization of the proposed network model and derive several passivity and synchronization criteria based on some inequality techniques. In addition, by considering the difficulty in achieving passivity (synchronization) in such a network, an adaptive control scheme is also developed to ensure that the proposed network achieves passivity (synchronization). Finally, we design two numerical examples to verify the effectiveness of the derived passivity and synchronization criteria.

Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.

An Online Minimax Optimal Algorithm for Adversarial Multiarmed Bandit Problem

We investigate the adversarial multiarmed bandit problem and introduce an online algorithm that asymptotically achieves the performance of the best switching bandit arm selection strategy. Our algorithms are truly online such that we do not use the game length or the number of switches of the best arm selection strategy in their constructions. Our results are guaranteed to hold in an individual sequence manner, since we have no statistical assumptions on the bandit arm losses. Our regret bounds, i.e., our performance bounds with respect to the best bandit arm selection strategy, are minimax optimal up to logarithmic terms. We achieve the minimax optimal regret with computational complexity only log-linear in the game length. Thus, our algorithms can be efficiently used in applications involving big data. Through an extensive set of experiments involving synthetic and real data, we demonstrate significant performance gains achieved by the proposed algorithm with respect to the state-of-the-art switching bandit algorithms. We also introduce a general efficiently implementable bandit arm selection framework, which can be adapted to various applications.

Dissipativity and Synchronization of Generalized BAM Neural Networks With Multivariate Discontinuous Activations

This paper is concerned with the dissipativity and synchronization problems of a class of delayed bidirectional associative memory (BAM) neural networks in which neuron activations are modeled by discontinuous bivariate functions. First, the concept of the Filippov solution is extended to functional differential equations with discontinuous right-hand sides and mixed delays via functional differential inclusions. The global dissipativity of the Filippov solution to the considered BAM neural networks is proven using generalized Halanay inequalities and matrix measure approaches. Second, to realize global exponential complete synchronization of BAM neural networks with multivariate discontinuous activations, discontinuous state feedback controllers are designed using functional differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov functional method. Finally, several numerical examples are provided to demonstrate the applicability and effectiveness of our proposed results.

Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty

This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous activation function) under uncertainty. It is worth noting that there exist few results about FNNs with discontinuous activation functions, which is mainly because classical solutions and theories of differential equations cannot be applied in this case. Especially, there is no relevant finite-time stabilization research for such system, and this paper makes up for the gap. The existence of global solution under the framework of Filippov for such system is guaranteed by limiting discontinuous activation functions. According to set-valued analysis and Kakutani's fixed point theorem, we obtain the existence of equilibrium point. In particular, based on differential inclusion theory and fractional Lyapunov stability theory, several new sufficient conditions are given to ensure finite-time stabilization via a novel discontinuous controller, and the upper bound of the settling time for stabilization is estimated. In addition, we analyze the finite-time stabilization of FNNs with Lipschitz-continuous activation functions under uncertainty. The results of this paper improve corresponding ones of integer-order neural networks with discontinuous and continuous activation functions. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

Synchronization Criteria for Discontinuous Neural Networks With Mixed Delays via Functional Differential Inclusions

This paper investigates the issue of global exponential synchronization for a class of general neural networks that contains discontinuous activation functions and mixed time delays. Functional differential inclusions and nonsmooth analysis theories are used as bases to design discontinuous controllers, such that the discontinuous neural networks can be exponential complete synchronized. This novel approach and its applicability to neural networks with continuous activations are also easily verified. Several numerical examples demonstrate the practicality and effectiveness of the design method.

Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topology via an Adaptive Approach

This paper investigates the synchronization issue of coupled reaction-diffusion neural networks with directed topology via an adaptive approach. Due to the complexity of the network structure and the presence of space variables, it is difficult to design proper adaptive strategies on coupling weights to accomplish the synchronous goal. Under the assumptions of two kinds of special network structures, that is, directed spanning path and directed spanning tree, some novel edge-based adaptive laws, which utilized the local information of node dynamics fully are designed on the coupling weights for reaching synchronization. By constructing appropriate energy function, and utilizing some analytical techniques, several sufficient conditions are given. Finally, some simulation examples are given to verify the effectiveness of the obtained theoretical results.

Observer-Based Robust Coordinated Control of Multiagent Systems With Input Saturation

This paper addresses the robust semiglobal coordinated control of multiple-input multiple-output multiagent systems with input saturation together with dead zone and input additive disturbance. Observer-based coordinated control protocol is constructed, by combining the parameterized low-and-high-gain feedback technique and the high-gain observer design approach. It is shown that, under some mild assumptions on agents' intrinsic dynamics, the robust semiglobal consensus or robust semiglobal swarm can be approached for undirected connected multiagent systems. Then, specific guidelines on the selection of the low-gain parameter, the high-gain parameter, and the high-gain observer gain have been provided. At last, numerical simulations are presented to illustrate the theoretical results.

Finite-Time Stabilization of Delayed Memristive Neural Networks: Discontinuous State-Feedback and Adaptive Control Approach

In this paper, a general class of delayed memristive neural networks (DMNNs) system described by functional differential equation with discontinuous right-hand side is considered. Under the extended Filippov-framework, we investigate the finite-time stabilization problem for DMNNs by using the famous finite-time stability theorem and the generalized Lyapunov functional method. To do so, we design two classes of novel controllers including discontinuous state-feedback controller and discontinuous adaptive controller. Without assuming the boundedness and monotonicity of the activation functions, several sufficient conditions are given to stabilize the states of this class of DMNNs in finite time. Moreover, the upper bounds of the settling time for stabilization are estimated. Finally, numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results.

Passivity and Output Synchronization of Complex Dynamical Networks With Fixed and Adaptive Coupling Strength

This paper considers a complex dynamical network model, in which the input and output vectors have different dimensions. We, respectively, investigate the passivity and the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed and adaptive coupling strength. First, two new passivity definitions are proposed, which generalize some existing concepts of passivity. By constructing appropriate Lyapunov functional, some sufficient conditions ensuring the passivity, input strict passivity and output strict passivity are derived for the complex dynamical network with fixed coupling strength. In addition, we also reveal the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed coupling strength. By employing the relationship between output strict passivity and output synchronization, a sufficient condition for output synchronization of the complex dynamical network with fixed coupling strength is established. Then, we extend these results to the case when the coupling strength is adaptively adjusted. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the proposed criteria.