Stability criteria for stochastic Takagi‐Sugeno fuzzy Cohen‐Grossberg BAM neural networks with mixed time‐varying delays

This article is concerned with the asymptotic stability analysis of Takagi–Sugeno stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed time‐varying delays. Based on the Lyapunov functional and linear matrix inequality (LMI) technique, sufficient conditions are derived to ensure the global convergence of the equilibrium point. The proposed conditions can be checked easily by LMI Control Toolbox in Matlab. It has been shown that the results are less restrictive than previously known criteria. They are obtained under mild conditions, assuming neither differentiability nor strict monotonicity for activation function. Numerical examples are given to demonstrate the effectiveness of our results. © 2014 Wiley Periodicals, Inc. Complexity 21: 143–154, 2016     

Analysis of stability for impulsive fuzzy Cohen–Grossberg BAM neural networks with delays

In this paper, based on the topological degree theory, Lyapunov functional method and inequality analysis technique, the existence and global exponential stability of equilibrium of impulsive fuzzy Cohen–Grossberg bi‐directional associative memory neural networks with delays, are investigated. Moreover, an illustrative example is given to demonstrate the effectiveness of the results obtained. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust asymptotic state estimation of Takagi–Sugeno fuzzy Markovian jumping Hopfield neural networks with mixed interval time‐varying delays

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the state estimation of uncertain Markovian jumping Hopfield neural networks with mixed interval time‐varying delays. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delays, the dynamics of the estimation error are globally asmptotically stable in the mean square. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, several delay‐dependent robust state estimators for such T–S fuzzy Markovian jumping Hopfield neural networks can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. Finally a numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

Robust dissipativity and passivity analysis for discrete‐time stochastic neural networks with time‐varying delay

In this article, we consider the problem of robust dissipativity and passivity analysis for a class of general discrete‐time recurrent neural networks (NNs) with time‐varying delays. The NN under consideration is subject to time‐varying and norm bounded parameter uncertainties. By the latest free‐weighting matrix method, an appropriate Lyapunov–Krasovskii functional and using stochastic analysis technique a sufficient condition is established to ensure that the NNs under consideration is strictly ‐dissipative. The derived conditions are presented in terms of linear matrix inequalities. Numerical examples and its simulations are given to demonstrate the effectiveness of the results. © 2014 Wiley Periodicals, Inc. Complexity 21: 47–58, 2016     

Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen–Grossberg neural networks

This article is concerned with the existence and robust stability of an equilibrium point that related to interval inertial Cohen–Grossberg neural networks. Such condition requires the existence of an equilibrium point to a given system, so the existence and uniqueness of the equilibrium point are emerged via nonlinear measure method. Furthermore, with the help of Halanay inequality lemma, differential mean value theorem as well as inequality technique, several sufficient criteria are derived to ascertain the robust stability of the equilibrium point for the addressed system. The results obtained in this article will be shown to be new and they can be considered alternative results to previously results. Finally, the effectiveness and computational issues of the two models for the analysis are discussed by two examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 459–469, 2016     

A delay decomposition approach for robust dissipativity and passivity analysis of neutral‐type neural networks with leakage time‐varying delay

This article presents the robust dissipativity and passivity analysis of neutral‐type neural networks with leakage time‐varying delay via delay decomposition approach. Using delay decomposition technique, new delay‐dependent criteria ensuring the considered system to be ‐γ dissipative are established in terms of strict linear matrix inequalities. A new Lyapunov–Krasovskii functional is constructed by dividing the discrete and neutral delay intervals into m and l segments, respectively, and choosing different Lyapunov functionals to different segments. Further, the dissipativity behaviors of neural networks which are affected due to the sensitiveness of the time delay in the leakage term have been taken into account. Finally, numerical examples are provided to show the effectiveness of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 248–264, 2016     

Stability analysis in Lagrange sense for a non-autonomous Cohen–Grossberg neural network with mixed delays

The paper discusses the global exponential stability in the Lagrange sense for a non-autonomous Cohen–Grossberg neural network (CGNN) with time-varying and distributed delays. The boundedness and global exponential attractivity of non-autonomous CGNN with time-varying and distributed delays are investigated by constructing appropriate Lyapunov-like functions. Moreover, we provide verifiable criteria on the basis of considering three different types of activation function, which include both bounded and unbounded activation functions. These results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. In the end, an illustrative example is given to verify our results.     

Further results on exponential stability of discrete‐time BAM neural networks with time‐varying delays

This paper is concerned with the exponential stability for the discrete‐time bidirectional associative memory neural networks with time‐varying delays. Based on Lyapunov stability theory, some novel delay‐dependent sufficient conditions are obtained to guarantee the globally exponential stability of the addressed neural networks. In order to obtain less conservative results, an improved Lyapunov–Krasovskii functional is constructed and the reciprocally convex approach and free‐weighting matrix method are employed to give the upper bound of the difference of the Lyapunov–Krasovskii functional. Several numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust stability analysis of stochastic neural networks with Markovian jumping parameters and probabilistic time‐varying delays

This article discusses the issue of robust stability analysis for a class of Markovian jumping stochastic neural networks (NNs) with probabilistic time‐varying delays. The jumping parameters are represented as a continuous‐time discrete‐state Markov chain. Using the stochastic stability theory, properties of Brownian motion, the information of probabilistic time‐varying delay, the generalized Ito's formula, and linear matrix inequality (LMI) technique, some novel sufficient conditions are obtained to guarantee the stochastical stability of the given NNs. In particular, the activation functions considered in this article are reasonably general in view of the fact that they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. The main features of this article are described in the following: first one is that, based on generalized Finsler lemma, some improved delay‐dependent stability criteria are established and the second one is that the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established using an efficient LMI approach. Finally, two numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–72, 2016     

Delay decomposition approach to state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters

This paper investigates the state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. On the basis of the new Lyapunov–Krasovskii functional, some inequality techniques, stochastic stability theory and delay‐dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

New delay‐dependent global robust passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays

The problem of passivity analysis for stochastic neural networks with Markovian jumping parameters and interval time‐varying delays is investigated in this article. By constructing a novel Lyapunov–Krasovskii functional based on the complete delay‐decomposing idea and using improved free‐weighting matrix method, some improved delay‐dependent passivity criteria are established in terms of linear matrix inequalities. Numerical examples are also given to show the effectiveness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 167–179, 2016     

Cluster synchronization for T–S fuzzy complex networks using pinning control with probabilistic time‐varying delays

In this article, cluster synchronization problem for Lur'e type Takagi–Sugeno (T–S) fuzzy complex networks with probabilistic time‐varying delays is considered. Pinning control strategy is proposed. The probability distribution of the time‐varying delay is considered. In terms of the probability distribution of the delays, a new type of system model with probability‐distribution‐dependent parameter matrices is proposed. Moreover, probabilistic delay is assumed to satisfy certain probability distribution and the probability of the delay takes values in some intervals. By constructing a suitable Lyapunov–Krasovskii functional involving triple integral terms and using Kronecker product with convex combination technique, some sufficient conditions are derived to ensure the cluster synchronization of designed networks such that the linear feedback controller can be used to every cluster. The problem of controller design is converted into solving a series of linear matrix inequalities. The effectiveness of our results is verified through numerical examples and simulations. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–77, 2015     

Robust stability results for nonlinear Markovian jump systems with mode‐dependent time‐varying delays and randomly occurring uncertainties

This article is concerned with the robust stability analysis for Markovian jump systems with mode‐dependent time‐varying delays and randomly occurring uncertainties. Sufficient delay‐dependent stability results are derived with the help of stability theory and linear matrix inequality technique using direct delay‐decomposition approach. Here, the delay interval is decomposed into two subintervals using the tuning parameter η such that , and the sufficient stability conditions are derived for each subintervals. Further, the parameter uncertainties are assumed to be occurring in a random manner. Numerical examples are given to validate the derived theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 50–60, 2016     

Dissipativity analysis of memristive neural networks with time‐varying delays and randomly occurring uncertainties

Dissipativity theory is a very important concept in the field of control system. In this paper, we pay attention to the problem of dissipativity analysis of memristive neural networks with time‐varying delay and randomly occurring uncertainties(ROUs). Under the framework of Filippov solution, differential inclusion theory, by employing a proper Lyapunov functional, and some inequality techniques, the dissipativity criteria are obtained in terms of LMIs. It should be noteworthy that the uncertainty terms as well as the ROUs are separately taken into consideration, in which the uncertainties are norm‐bounded and the ROUs obey certain mutually uncorrelated Bernoulli‐distributed white noise sequences. Finally, the effectiveness of the proposed method will be verified via numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

State estimation of memristor‐based recurrent neural networks with time‐varying delays based on passivity theory

This article deals with the state estimation problem of memristor‐based recurrent neural networks (MRNNs) with time‐varying delay based on passivity theory. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time delay, the dynamics of the estimation error is passive from the control input to the output error. Based on the Lyapunov–Krasovskii functional (LKF) involving proper triple integral terms, convex combination technique, and reciprocal convex technique, a delay‐dependent state estimation of MRNNs with time‐varying delay is established in terms of linear matrix inequalities (LMIs). The information about the neuron activation functions and lower bound of the time‐varying delays is fully used in the LKF. Then, the desired estimator gain matrix is accomplished by solving LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed theoretical results. © 2013 Wiley Periodicals, Inc. Complexity 19: 32–43, 2014     

Dynamical analysis of impulsive neural networks with time‐varying delays

In this work, a new criterion concerning the global exponential stability of impulsive neural networks with time‐varying delays is presented by employing the impulsive delayed differential inequality method. The criterion is independent of the time‐varying delays and does not require the differentiability of delay functions. An example and its simulation showing the effectiveness of the present criterion is given finally. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiple‐interval‐dependent robust stability analysis for uncertain stochastic neural networks with mixed‐delays

This article deals with the problem of robust stochastic asymptotic stability for a class of uncertain stochastic neural networks with distributed delay and multiple time‐varying delays. It is noted that the reciprocally convex approach has been intensively used in stability analysis for time‐delay systems in the past few years. We will extend the approach from deterministic time‐delay systems to stochastic time‐delay systems. And based on the new technique dealing with matrix cross‐product and multiple‐interval‐dependent Lyapunov–Krasovskii functional, some novel delay‐dependent stability criteria with less conservatism and less decision variables for the addressed system are derived in terms of linear matrix inequalities. At last, several numerical examples are given to show the effectiveness of the results. © 2014 Wiley Periodicals, Inc. Complexity 21: 147–162, 2015     

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode‐dependent probabilistic time‐varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time‐varying delay is considered and transformed into one with deterministic time‐varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov‐Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple‐integral term is introduced for deriving the delay‐dependent stability conditions. Furthermore, mode‐dependent mean square exponential stability criteria are derived by constructing a new Lyapunov‐Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 39–65, 2015     

Existence and exponential stability of almost‐periodic solutions for neutral BAM neural networks with time‐varying delays in leakage terms on time scales

This paper is concerned with neutral bidirectional associative memory neural networks with time‐varying delays in leakage terms on time scales. Some sufficient conditions on the existence, uniqueness, and global exponential stability of almost‐periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.