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.     

Exponential stability of Hopfield neural networks with time‐varying delays via impulsive control

In this paper, by utilizing the Lyapunov functionals, the analysis method and the impulsive control, we analyze the exponential stability of Hopfield neural networks with time‐varying delays. A new criterion on the exponential stabilization by impulses and the exponential stabilization by periodic impulses is gained. We can see that impulses do contribution to the system's exponential stability. Two examples are given to illustrate the effectiveness of our result. Copyright © 2010 John Wiley & Sons, Ltd.     

Global exponential stability of fractional‐order impulsive neural network with time‐varying and distributed delay

In this article, we present several results on global exponential stability of a fractional‐order cellular neural network with impulses and with time‐varying and distributed delay. By using the Lyapunov‐like function methods in conjunction with the Razumikhin techniques, we derive sufficient condition for the exponential stability with an exponential convergence rate. The obtained outcomes of our present investigation significantly extend and generalize the corresponding results existing in the current literature. Finally, we give 2 illustrative examples to demonstrate the theoretical findings.     

Finite‐time synchronization of memristive neural networks with time‐varying delays via two control methods

In this paper, on the basis of the Lyapunov stability theory and finite‐time stability lemma, the finite‐time synchronization problem for memristive neural networks with time‐varying delays is studied by two control methods. First, the discontinuous state‐feedback control rule containing integral part for square sum of the synchronization error and the discontinuous adaptive control rule are designed for realizing synchronization of drive‐response memristive neural networks in finite time, respectively. Then, by using some important inequalities and defining suitable Lyapunov functions, some algebraic sufficient criteria guaranteeing finite‐time synchronization are deduced for drive‐response memristive neural networks in finite time. Furthermore, we give the estimation of the upper bounds of the settling time of finite‐time synchronization. Lastly, the effectiveness of the obtained sufficient criteria guaranteeing finite‐time synchronization is validated by simulation.     

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     

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     

Intermittent impulsive projective synchronization in time‐varying delayed dynamical network with variable structures

This paper studies the projective synchronization behavior in a drive‐response dynamical network with coupling time‐varying delay via intermittent impulsive control. Different from the most publications on drive‐response dynamical networks under the general impulsive control, here the impulsive effects can only exist at control windows, not during the whole time. Moreover, intermittent impulsive control does not need the limitation of the upper bound of the impulsive intervals. By utilizing the Lyapunov‐Razumikhin technique, some sufficient conditions for the projective synchronization are derived. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results. © 2016 Wiley Periodicals, Inc. Complexity 21: 547–556, 2016     

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.     

Non‐fragile synchronization control for complex networks with additive time‐varying delays

In this article, a synchronization problem for complex dynamical networks with additive time‐varying coupling delays via non‐fragile control is investigated. A new class of Lyapunov–Krasovskii functional with triple integral terms is constructed and using reciprocally convex approach, some new delay‐dependent synchronization criteria are derived in terms of linear matrix inequalities (LMIs). When applying Jensen's inequality to partition double integral terms in the derivation of LMI conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. To handle such a combination, an effective method is introduced by extending the lower bound lemma. Then, a sufficient condition for designing the non‐fragile synchronization controller is introduced. Finally, a numerical example is given to show the advantages of the proposed techniques. © 2014 Wiley Periodicals, Inc. Complexity 21: 296–321, 2015     

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     

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     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015     

A new criterion to global exponential stability for impulsive neural networks with continuously distributed delays

This paper considers the global exponential stability and exponential convergence rate of impulsive neural networks with continuously distributed delays in which the state variables on the impulses are related to the unbounded distributed delays. By establishing a new impulsive delay differential inequality, a new criterion concerning global exponential stability for these networks is derived, and the estimated exponential convergence rate is also obtained. The result extends and improves on earlier publications. In addition, two numerical examples are given to illustrate the applicability of the result. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

μ‐stability of impulsive differential systems with unbounded time‐varying delays and nonlinear perturbations

This paper is concerned with the problem of μ‐stability of impulsive differential systems with unbounded time‐varying delays and nonlinear perturbations. Some μ‐stability criteria, which depend on the range of distributed delay and the decay rate of discrete delay (not the range), are derived by using Lyapunov–Krasovski functional method. Those criteria are expressed in the form of linear matrix inequalities and they can easily be checked. Two numerical examples are provided to demonstrate the effectiveness of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

synchronization of coupled reaction‐diffusion neural networks with mixed delays

The reaction‐diffusion neural network is often described by semilinear diffusion partial differential equation (PDE). This article focuses on the asymptotical synchronization and synchronization for coupled reaction‐diffusion neural networks with mixed delays (that is, discrete and infinite distributed delays) and Dirichlet boundary condition. First, using the Lyapunov–Krasoviskii functional scheme, the sufficient condition is obtained for the asymptotical synchronization of coupled semilinear diffusion PDEs with mixed time‐delays and this condition is represented by linear matrix inequalities (LMIs), which is easy to be solved. Then the robust synchronization is considered in temporal‐spatial domain for the coupled semilinear diffusion PDEs with mixed delays and external disturbances. In terms of the technique of completing squares, the sufficient condition is obtained for the robust synchronization. Finally, a numerical example of coupled semilinear diffusion PDEs with mixed time‐delays is given to illustrate the correctness of the obtained results. © 2016 Wiley Periodicals, Inc. Complexity 21: 42–53, 2016     

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     

Mean square exponential stability in high-order stochastic impulsive neural networks with time-varying delays

In this paper, we consider a class of stochastic impulsive high-order neural networks with time-varying delays. By using Lyapunov functional method, LMI method and mathematics induction, some sufficient conditions are derived for the globally exponential stability of the equilibrium point of the neural networks in mean square. It is believed that these results are significant and useful for the design and applications of impulsive stochastic high-order neural networks.     

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