Stability Analysis of Discrete-Time Neural Networks With Time-Varying Delay via an Extended Reciprocally Convex Matrix Inequality

This paper is concerned with the stability analysis of discrete-time neural networks with a time-varying delay. Assessment of the effect of time delays on system stability requires suitable delay-dependent stability criteria. This paper aims to develop new stability criteria for reduction of conservatism without much increase of computational burden. An extended reciprocally convex matrix inequality is developed to replace the popular reciprocally convex combination lemma (RCCL). It has potential to reduce the conservatism of the RCCL-based criteria without introducing any extra decision variable due to its advantage of reduced estimation gap using the same decision variables. Moreover, a delay-product-type term is introduced for the first time into the Lyapunov function candidate such that a delay-variation-dependent stability criterion with the bounds of delay change rate is established. Finally, the advantages of the proposed criteria are demonstrated through two numerical examples.

Reachable Set Estimation for Markovian Jump Neural Networks With Time-Varying Delays

In this paper, the reachable set estimation problem is investigated for Markovian jump neural networks (NNs) with time-varying delays and bounded peak disturbances. Our goal is to find a set as small as possible which bounds all the state trajectories of the NNs under zero initial conditions. In the framework of Lyapunov-Krasovskii theorem, a newly-found summation inequality combined with the reciprocally convex approach is used to bound the difference of the proposed Lyapunov functional. A new less conservative condition dependent on the upper bound, the lower bound and the delay range of the time delay is established to guarantee that the state trajectories are bounded within an ellipsoid-like set. Then the result is extended to the case with incomplete transition probabilities and a more general condition is derived. Finally, examples including a genetic regulatory network are given to demonstrate the usefulness and the effectiveness of the results obtained in this paper.

Synchronization stability of memristor-based complex-valued neural networks with time delays

This paper focuses on the dynamical property of a class of memristor-based complex-valued neural networks (MCVNNs) with time delays. By constructing the appropriate Lyapunov functional and utilizing the inequality technique, sufficient conditions are proposed to guarantee exponential synchronization of the coupled systems based on drive-response concept. The proposed results are very easy to verify, and they also extend some previous related works on memristor-based real-valued neural networks. Meanwhile, the obtained sufficient conditions of this paper may be conducive to qualitative analysis of some complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of our theoretical results.

Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays

This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.

Exponential Synchronization for Markovian Stochastic Coupled Neural Networks of Neutral-Type via Adaptive Feedback Control

In this paper, we investigate the adaptive exponential synchronization in both the mean square and the almost sure senses for an array of N identical Markovian stochastic coupled neural networks of neutral-type with time-varying delay and random coupling strength. The generalized Lyapunov theorem of the exponential stability in the mean square for the neutral stochastic Markov system with the time-varying delay is first established. The time-varying delay in the system is assumed to be a bounded measurable function. Then, sufficient conditions to guarantee the exponential synchronization in the mean square for the underlying system are developed under an adaptive feedback controller, which are given in terms of the M -matrix and the algebraic inequalities. Under the same conditions, the almost sure exponential synchronization is also presented. A numerical example is given to show the effectiveness and potential of the proposed theoretical results.

Impulsive Multisynchronization of Coupled Multistable Neural Networks With Time-Varying Delay

This paper studies the synchronization problem of coupled delayed multistable neural networks (NNs) with directed topology. To begin with, several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points. Then two new concepts named dynamical multisynchronization (DMS) and static multisynchronization (SMS) are introduced to describe the two novel kinds of synchronization manifolds. Using the impulsive control strategy and the Razumikhin-type technique, some sufficient conditions for both the DMS and the SMS of the controlled coupled delayed multistable NNs with fixed and switching topologies are derived, respectively. Simulation examples are presented to illustrate the effectiveness of the proposed results.

Non-fragile mixed H∞ and passive synchronization of Markov jump neural networks with mixed time-varying delays and randomly occurring controller gain fluctuation

This paper studies the non-fragile mixed H∞ and passive synchronization problem for Markov jump neural networks. The randomly occurring controller gain fluctuation phenomenon is investigated for non-fragile strategy. Moreover, the mixed time-varying delays composed of discrete and distributed delays are considered. By employing stochastic stability theory, synchronization criteria are developed for the Markov jump neural networks. On the basis of the derived criteria, the non-fragile synchronization controller is designed. Finally, an illustrative example is presented to demonstrate the validity of the control approach.

Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links

This paper is concerned with the problem of extended dissipativity-based state estimation for discrete-time Markov jump neural networks (NNs), where the variation of the piecewise time-varying transition probabilities of Markov chain is subject to a set of switching signals satisfying an average dwell-time property. The communication links between the NNs and the estimator are assumed to be imperfect, where the phenomena of signal quantization and data packet dropouts occur simultaneously. The aim of this paper is to contribute with a Markov switching estimator design method, which ensures that the resulting error system is extended stochastically dissipative, in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links. Sufficient conditions for the solvability of such a problem are established. Based on the derived conditions, an explicit expression of the desired Markov switching estimator is presented. Finally, two illustrated examples are given to show the effectiveness of the proposed design method.

Distributed Consensus of Stochastic Delayed Multi-agent Systems Under Asynchronous Switching

In this paper, the distributed exponential consensus of stochastic delayed multi-agent systems with nonlinear dynamics is investigated under asynchronous switching. The asynchronous switching considered here is to account for the time of identifying the active modes of multi-agent systems. After receipt of confirmation of mode's switching, the matched controller can be applied, which means that the switching time of the matched controller in each node usually lags behind that of system switching. In order to handle the coexistence of switched signals and stochastic disturbances, a comparison principle of stochastic switched delayed systems is first proved. By means of this extended comparison principle, several easy to verified conditions for the existence of an asynchronously switched distributed controller are derived such that stochastic delayed multi-agent systems with asynchronous switching and nonlinear dynamics can achieve global exponential consensus. Two examples are given to illustrate the effectiveness of the proposed method.

Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays

In this brief, the problems of the mixed H-infinity and passivity performance analysis and design are investigated for discrete time-delay neural networks with Markovian jump parameters represented by Takagi-Sugeno fuzzy model. The main purpose of this brief is to design a filter to guarantee that the augmented Markovian jump fuzzy neural networks are stable in mean-square sense and satisfy a prescribed passivity performance index by employing the Lyapunov method and the stochastic analysis technique. Applying the matrix decomposition techniques, sufficient conditions are provided for the solvability of the problems, which can be formulated in terms of linear matrix inequalities. A numerical example is also presented to illustrate the effectiveness of the proposed techniques.

Observer-based robust finite time H∞ sliding mode control for Markovian switching systems with mode-dependent time-varying delay and incomplete transition rate

This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem.

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

This paper is concerned with the finite-time synchronization issue of nonlinear coupled neural networks by designing a new switching pinning controller. For the fixed network topology and control strength, the newly designed controller could optimize the synchronization time by regulating a parameter α (0 ≤ α < 1). The control law presented in this paper covers both continuous controllers and discontinuous ones, which were studied separately in the past. Some criteria are discussed in detail on how to shorten the synchronization time for the strongly connected networks. Finally, the results are generalized to any network topologies containing a directed spanning tree, and one numerical example is given to demonstrate the effectiveness of the theoretical results.

Pinning Synchronization of Directed Networks With Switching Topologies: A Multiple Lyapunov Functions Approach

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from M -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results.

Mode-Dependent Stochastic Synchronization for Markovian Coupled Neural Networks With Time-Varying Mode-Delays

This paper investigates the stochastic synchronization problem for Markovian hybrid coupled neural networks with interval time-varying mode-delays and random coupling strengths. The coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is proposed, where some terms involving triple or quadruple integrals are considered, which makes the LKF matrices mode-dependent as much as possible. This gives significant improvement in the synchronization criteria, i.e., less conservative results can be obtained. In addition, by applying an extended Jensen's integral inequality and the properties of random variables, new delay-dependent synchronization criteria are derived. The obtained criteria depend not only on upper and lower bounds of mode-delays but also on mathematical expectations and variances of the random coupling strengths. Finally, two numerical examples are provided to demonstrate the feasibility of the proposed results.

Energy-to-peak state estimation for Markov jump RNNs with time-varying delays via nonsynchronous filter with nonstationary mode transitions

In this paper, the problem of energy-to-peak state estimation for a class of discrete-time Markov jump recurrent neural networks (RNNs) with randomly occurring nonlinearities (RONs) and time-varying delays is investigated. A practical phenomenon of nonsynchronous jumps between RNNs modes and desired mode-dependent filters is considered, and a nonstationary mode transition among the filters is used to model the nonsynchronous jumps to different degrees that are also mode dependent. The RONs are used to model a class of sector-like nonlinearities that occur in a probabilistic way according to a Bernoulli sequence. The time-varying delays are supposed to be mode dependent and unknown, but with known lower and upper bounds a priori. Sufficient conditions on the existence of the nonsynchronous filters are obtained such that the filtering error system is stochastically stable and achieves a prescribed energy-to-peak performance index. Further to the recent study on the class of nonsynchronous estimation problem, a monotonicity is observed in obtaining filtering performance index, while changing the degree of nonsynchronous jumps. A numerical example is presented to verify the theoretical findings.

Adaptive Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

In this paper, adaptive synchronization of memristor-based neural networks (MNNs) with time-varying delays is investigated. The dynamical analysis here employs results from the theory of differential equations with discontinuous right-hand sides as introduced by Filippov. Sufficient conditions for the global synchronization of MNNs are established with a general adaptive controller. The update gain of the controller can be adjusted to control the synchronization speed. The obtained results complement and improve the previously known results. Finally, numerical simulations are carried out to demonstrate the effectiveness of the obtained results.

Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control

In this paper, the synchronization problem for neural networks with stochastic perturbation is studied with intermittent control via adaptive aperiodicity. Under the framework of stochastic theory and Lyapunov stability method, we develop some techniques of intermittent control with adaptive aperiodicity to achieve the synchronization of a class of neural networks, modeled by stochastic systems. Some effective sufficient conditions are established for the realization of synchronization of the underlying network. Numerical simulations of two examples are provided to illustrate the theoretical results obtained in the paper.

Exponential Stabilization of Memristor-based Chaotic Neural Networks with Time-Varying Delays via Intermittent Control

This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results.

Exponential stabilization for sampled-data neural-network-based control systems

This paper investigates the problem of sampled-data stabilization for neural-network-based control systems with an optimal guaranteed cost. Using time-dependent Lyapunov functional approach, some novel conditions are proposed to guarantee the closed-loop systems exponentially stable, which fully use the available information about the actual sampling pattern. Based on the derived conditions, the design methods of the desired sampled-data three-layer fully connected feedforward neural-network-based controller are established to obtain the largest sampling interval and the smallest upper bound of the cost function. A practical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.