Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016     

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014     

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     

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     

Finite‐time synchronization of a class of N‐coupled complex partial differential systems with time‐varying delay

This study examines finite‐time synchronization for a class of N‐coupled complex partial differential systems (PDSs) with time‐varying delay. The problem of finite‐time synchronization for coupled drive‐response PDSs with time‐varying delay is similarly considered. The synchronization error dynamic of the PDSs is defined in the q‐dimensional spatial domain. We construct a feedback controller to achieve finite‐time synchronization. Sufficient conditions are derived by using the Lyapunov‐Krasoviskii stability approach and inequalities technology to ensure that the proposed networks achieve synchronization in finite time. The proposed systems demonstrate extensive application. Finally, an example is used to verify the theoretical results.     

Synchronization of complex networks with time‐varying inner coupling and outer coupling matrices

Synchronization of complex networks with time‐varying coupling matrices is studied in this paper. Two kinds of time‐varying coupling are taken into account. One is the time‐varying inner coupling in the node state space and the other is the time‐varying outer coupling in the network topology space. By respectively setting linear controllers and adaptive controllers, time‐varying complex networks can be synchronized to a desired state. Meanwhile, different influences of the control parameters of linear controllers and adaptive controllers on the synchronization have also been investigated. Based on the Lyapunov function theory, we construct appropriate positive‐definite functions, and several sufficient synchronization criteria are obtained. Numerical simulations further illustrate the effectiveness of conclusions. Copyright © 2017 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     

Delay-induced diversity of firing behavior and ordered chaotic firing in adaptive neuronal networks

In this paper, we study the effect of time delay on the firing behavior and temporal coherence and synchronization in Newman–Watts thermosensitive neuron networks with adaptive coupling. At beginning, the firing exhibit disordered spiking in absence of time delay. As time delay is increased, the neurons exhibit diversity of firing behaviors including bursting with multiple spikes in a burst, spiking, bursting with four, three and two spikes, firing death, and bursting with increasing amplitude. The spiking is the most ordered, exhibiting coherence resonance (CR)-like behavior, and the firing synchronization becomes enhanced with the increase of time delay. As growth rate of coupling strength or network randomness increases, CR-like behavior shifts to smaller time delay and the synchronization of firing increases. These results show that time delay can induce diversity of firing behaviors in adaptive neuronal networks, and can order the chaotic firing by enhancing and optimizing the temporal coherence and enhancing the synchronization of firing. However, the phenomenon of firing death shows that time delay may inhibit the firing of adaptive neuronal networks. These findings provide new insight into the role of time delay in the firing activity of adaptive neuronal networks, and can help to better understand the complex firing phenomena in neural networks.     

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     

Robust synchronization for stochastic delayed complex networks with switching topology and unmodeled dynamics via adaptive control approach

In this paper, the robust synchronization problem for a class of stochastic delayed complex networks with switching topology and unmodeled dynamics is investigated by using the adaptive control scheme. Different from some existing uncertain complex network models, the uncertain terms in the complex networks are only needed to be bounded. Based on the stability theory of stochastic delayed differential equation, a novel adaptive controller which ensures that all the nodes in the complex networks robustly synchronize with the target node is derived. Finally, a numerical example is provided to show the effectiveness of the proposed method.     

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     

Chaos projective synchronization of the chaotic finance system with parameter switching perturbation and input time‐varying delay

This paper discusses some basic dynamical properties of the chaotic finance system with parameter switching perturbation, and investigates chaos projective synchronization of the chaotic finance system with the time‐varying delayed feedback controller, which are not fully considered in the existing research. Different from the previous methods, in this paper, the delayed feedback controller is not only time‐varying, but also the time‐varying delay is adaptive. Finally, an illustrate example is provided to show the effectiveness of this method. Copyright © 2014 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     

Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays

This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results.     

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.     

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.     

Exponential synchronization of complex dynamical networks with markovian jump parameters and stochastic delays and its application to multi-agent systems

This paper studies the synchronization problem of complex dynamical networks with stochastic delay which switches stochastically among several forms of time-varying delays. Both the discrete and distributed delays are considered, as well as the Markovian jump parameters. The occurrence probability distribution of the stochastic delay is assumed to be known in prior. By utilizing the Lyapunov–Krasovskii stability theory and stochastic analysis techniques, some sufficient exponential synchronization criteria are obtained, which depend not only on the size of delays, but also on the occurrence probability distribution of the stochastic delay. Moreover, the main results are successfully extended to multi-agent systems with stochastic delay. Several numerical examples are given to illustrate the feasibility and effectiveness of the proposed methods.     

Design of observers for nonlinear systems with H ∞ performance analysis

This paper investigates the problem of observer design for nonlinear systems. By using differential mean value theorem, which allows transforming a nonlinear error dynamics into a linear parameter varying system, and based on Lyapunov stability theory, an approach of observer design for a class of nonlinear systems with time‐delay is proposed. The sufficient conditions, which guarantee the estimation error to asymptotically converge to zero, are given. Furthermore, an adaptive observer design for a class of nonlinear system with unknown parameter is considered. A method of H _∞ adaptive observer design is presented for this class of nonlinear systems; the sufficient conditions that guarantee the convergence of estimation error and the computing method for observer gain matrix are given. Finally, an example is given to show the effectiveness of our proposed approaches. Copyright © 2013 John Wiley & Sons, Ltd.     

Robust consensus of nonlinear multi‐agent systems via reliable control with probabilistic time delay

In this paper, the consensus problem of uncertain nonlinear multi‐agent systems is investigated via reliable control in the presence of probabilistic time‐varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time‐varying delay is equivalently transformed into the deterministic time‐varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed‐loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed‐loop system is robustly stable in the sense of mean‐square. For this purpose, through construction of a suitable Lyapunov–Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay‐dependent consensus stabilizability conditions for the closed‐loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 138–150, 2016     

On contraction of nonlinear difference equations with time‐varying delays

General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are derived. Finally, the obtained results are applied to time‐varying discrete‐time neural networks with delay.