New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay

Input-to-State Stability for Time-Delay Systems With Large Delays

In this article, we consider the input-to-state stability (ISS) problem for a class of time-delay systems with intermittent large delays, which may cause the invalidation of traditional delay-dependent stability criteria. The topic of this article features that it proposes a novel kind of stability criterion for time-delay systems, which is delay dependent if the time delay is smaller than a prescribed allowable size. While if the time delay is larger than the allowable size, the ISS can be preserved as well provided that the large-delay periods satisfy the kind of duration condition. Different from existing results on similar topics, we present the main result based on a unified Lyapunov-Krasovskii function (LKF). In this way, the frequency restriction can be removed and the analysis complexity can be simplified. A numerical example is provided to verify the proposed results.

State Estimation for Discrete Time-Delayed Impulsive Neural Networks Under Communication Constraints: A Delay-Range-Dependent Approach

In this article, a delay-range-dependent approach is put forward to tackle the state estimation problem for delayed impulsive neural networks. A new type of nonlinear function, which is more general than the normal sigmoid function and functions constrained by the Lipschitz condition, is adopted as the neuron activation function. To effectively alleviate data collisions and save energy, the round-robin protocol is utilized to mitigate the occurrence of unnecessary network congestion in communication channels from sensors to the estimator. With the aid of the Lyapunov stability theory, a state observer is constructed such that the estimation error dynamics are asymptotically stable. The observer existence is ensured by resorting to a set of delay-range-dependent criteria which is dependent on both the impulsive time instant and a coefficient matrix. In addition, the synthesis of the observer is discussed by using linear matrix inequalities. Simulations are provided to illustrate the reasonability of our delay-range-dependent estimation approach.

Multistability of Dynamic Memristor Delayed Cellular Neural Networks With Application to Associative Memories

Recently, dynamic memristor (DM)-cellular neural networks (CNNs) have received widespread attention due to their advantage of low power consumption. The previous works showed that DM-CNNs have at most 318 equilibrium points (EPs) with n=16 cells. Since time delay is unavoidable during the process of information transmission, the goal of this article is to research the multistability of DM-CNNs with time delay, and, meanwhile, to increase the storage capacity of DM-delay (D)CNNs. Depending on the different constitutive relations of memristors, two cases of the multistability for DM-DCNNs are discussed. After determining the constitutive relations, the number of EPs of DM-DCNNs is increased to 3ⁿ with n cells by means of the appropriate state-space decomposition and the Brouwer's fixed point theorem. Furthermore, the enlarged attraction domains of EPs can be obtained, and 2ⁿ of these EPs are locally exponentially stable in two cases. Compared with standard CNNs, the dynamic behavior of DM-DCNNs shows an outstanding merit. That is, the value of voltage and current approach to zero when the system becomes stable, and the memristor provides a nonvolatile memory to store the computation results. Finally, two numerical simulations are presented to illustrate the effectiveness of the theoretical results, and the applications of associative memories are shown at the end of this article.

Synchronization of Fractional Stochastic Chaotic Systems via Mittag-Leffler Function

This paper is involved with synchronization of fractional order stochastic systems in finite dimensional space, and we have tested its time response and stochastic chaotic behaviors. Firstly, we give a representation of solution for a stochastic fractional order chaotic system. Secondly, some useful sufficient conditions are investigated by using matrix type Mittag-Leffler function, Jacobian matrix via stochastic process, stability analysis and feedback control technique to assure the synchronization of stochastic error system. Thereafter, numerical illustrations are provided to verify the theoretical parts.

Stability and dissipativity criteria for neural networks with time-varying delays via an augmented zero equality approach

This work investigates the stability and dissipativity problems for neural networks with time-varying delay. By the construction of new augmented Lyapunov-Krasovskii functionals based on integral inequality and the use of zero equality approach, three improved results are proposed in the forms of linear matrix inequalities. And, based on the stability results, the dissipativity analysis for NNs with time-varying delays was investigated. Through some numerical examples, the superiority and effectiveness of the proposed results are shown by comparing the existing works.

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.

Omnidirectional Mobile Robot Dynamic Model Identification by NARX Neural Network and Stability Analysis Using the APLF Method

In this paper, the NARX neural network system is used to identify the complex dynamics model of omnidirectional mobile robot while rotating with moving, and analyze its stability. When the mobile robot model rotates and moves at the same time, the dynamic model of the mobile robot is complex and there is motion coupling. The change of the model in different states is a kind of symmetry. In order to solve the problem that there is a big difference between the mechanism modeling motion simulation and the actual data, the dynamic model identification of mobile robot in special state based on NARX neural network is proposed, and the stability analysis method is given. To verify that the dynamic model of NARX identification is consistent with that of the mobile robot, the Activation Path-Dependent Lyapunov Function (APLF) algorithm is used to distinguish the NARX neural network model expressed by LDI. However, the APLF method needs to calculate a large number of LMIs in practice and takes a lot of time, and, to solve this problem, an optimized APLF method is proposed. The experimental results verify the effectiveness of the theoretical method.

Reachable set bounding for neural networks with mixed delays: Reciprocally convex approach

This paper discusses the reachable set estimation problem of neural networks with mixed delays. Firstly, by means of the maximal Lyapunov-Krasovskii functional, we obtain a non-ellipsoid form of the reachable set. Further more, when calculating the derivative of the maximum Lyapunov functional, the lower bound lemma and reciprocally convex approach method are used to solve the reciprocally convex combination term, which reduce the related decision variables. Secondly, we extend the results to polytopic uncertainties neural networks and consider the case of uncertain differentiable parameters. Finally, two numerical examples and one application example are listed to show the validity of our methods.

Stability Analysis for Neural Networks With Time-Varying Delay via Improved Techniques

This paper is concerned with the stability problem for neural networks with a time-varying delay. First, an improved generalized free-weighting-matrix integral inequality is proposed, which encompasses the conventional one as a special case. Second, an improved Lyapunov-Krasovskii functional is constructed that contains two complement triple-integral functionals. Third, based on the improved techniques, a new stability condition is derived for neural networks with a time-varying delay. Finally, two widely used numerical examples are given to demonstrate that the proposed stability condition is very competitive in both conservatism and complexity.

th Moment Exponential Input-to-State Stability of Delayed Recurrent Neural Networks With Markovian Switching via Vector Lyapunov Function

In this paper, the th moment input-to-state exponential stability for delayed recurrent neural networks (DRNNs) with Markovian switching is studied. By using stochastic analysis techniques and classical Razumikhin techniques, a generalized vector -operator differential inequality including cross item is obtained. Without additional restrictive conditions on the time-varying delay, the sufficient criteria on the th moment input-to-state exponential stability for DRNNs with Markovian switching are derived by means of the vector -operator differential inequality. When the input is zero, an improved criterion on exponential stability is obtained. Two numerical examples are provided to examine the correctness of the derived results.

Design of robust reliable control for T-S fuzzy Markovian jumping delayed neutral type neural networks with probabilistic actuator faults and leakage delays: An event-triggered communication scheme

This study examines the problem of robust reliable control for Takagi-Sugeno (T-S) fuzzy Markovian jumping delayed neural networks with probabilistic actuator faults and leakage terms. An event-triggered communication scheme. First, the randomly occurring actuator faults and their failures rates are governed by two sets of unrelated random variables satisfying certain probabilistic failures of every actuator, new type of distribution based event triggered fault model is proposed, which utilize the effect of transmission delay. Second, Takagi-Sugeno (T-S) fuzzy model is adopted for the neural networks and the randomness of actuators failures is modeled in a Markov jump model framework. Third, to guarantee the considered closed-loop system is exponential mean square stable with a prescribed reliable control performance, a Markov jump event-triggered scheme is designed in this paper, which is the main purpose of our study. Fourth, by constructing appropriate Lyapunov-Krasovskii functional, employing Newton-Leibniz formulation and integral inequalities, several delay-dependent criteria for the solvability of the addressed problem are derived. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones, among them one example was supported by real-life application of the benchmark problem.

Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks

This paper deals with the global exponential stability for delayed recurrent neural networks (DRNNs). By constructing an augmented Lyapunov-Krasovskii functional and adopting the reciprocally convex combination approach and Wirtinger-based integral inequality, delay-dependent global exponential stability criteria are derived in terms of linear matrix inequalities. Meanwhile, a general and effective method on global exponential stability analysis for DRNNs is given through a lemma, where the exponential convergence rate can be estimated. With this lemma, some global asymptotic stability criteria of DRNNs acquired in previous studies can be generalized to global exponential stability ones. Finally, a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results.

Neural Network-Based Passive Filtering for Delayed Neutral-Type Semi-Markovian Jump Systems

This paper investigates the problem of exponential passive filtering for a class of stochastic neutral-type neural networks with both semi-Markovian jump parameters and mixed time delays. Our aim is to estimate the states by designing a Luenberger-type observer, such that the filter error dynamics are mean-square exponentially stable with an expected decay rate and an attenuation level. Sufficient conditions for the existence of passive filters are obtained, and a convex optimization algorithm for the filter design is given. In addition, a cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem, which can be readily solved by the existing optimization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed techniques.

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.

Stability Analysis of Neural Networks With Two Delay Components Based on Dynamic Delay Interval Method

In this paper, a dynamic delay interval (DDI) method is proposed to deal with the stability problem of neural networks with two delay components. This method extends the fixed interval of a time-varying delay to a dynamic one, which relaxes the restriction on upper and lower bounds of the delay intervals. Combining the reciprocally convex combination technique and Wirtinger integral inequality, the DDI method leads to some much less conservative delay-dependent stability criteria based on a linear matrix inequality for neural networks with two delay components. Furthermore, the criteria for the system with a single time-varying delay are provided. Some examples are given to illustrate the effectiveness of the obtained results.

Exponential stability of memristor-based synchronous switching neural networks with time delays

In this paper, we study the existence, uniqueness and stability of memristor-based synchronous switching neural networks with time delays. Several criteria of exponential stability are given by introducing multiple Lyapunov functions. In comparison with the existing publications on simplice memristive neural networks or switching neural networks, we consider a system with a series of switchings, these switchings are assumed to be synchronous with memristive switching mechanism. Moreover, the proposed stability conditions are straightforward and convenient and can reflect the impact of time delay on the stability. Two examples are also presented to illustrate the effectiveness of the theoretical results.