Kun She

New result on synchronization of complex dynamical networks with time-varying coupling delay and sampled-data control

In this paper, the sampled-data synchronization control problem is investigated for complex dynamical networks (CDNs) with time-varying coupling delay. By constructing a suitable Lyapunov-Krasovskii functional containing some novel triple integral terms with sufficient information about the actual sampling pattern, and together with a general inverse of first-order technique and some effective integral inequalities, less conservative conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the synchronization of sampled-data CDNs with time-varying coupling delay. Numerical examples are provided to illustrate the effectiveness and less conservativeness of the proposed approaches.

Finite-time lag synchronization of master-slave complex dynamical networks with unknown signal propagation delays

Abstract This paper studies the finite-time lag synchronization issue of master-slave complex networks with unknown signal propagation delays by the linear and adaptive error state feedback approaches. The unknown signal propagation delays are fully considered and estimated by adaptive laws. By designing new Lyapunov functional and discontinuous feedback controllers, which involves the estimated error rather than the general synchronization error, sufficient conditions are derived to ensure lag synchronization of the networks within a setting time. It is interesting to discover that the setting time is related to initial values of both the estimated error and the estimated unknown signal propagation delays. Finally, two numerical examples are given to illustrate the effectiveness and correctness of the proposed finite-time lag synchronization criteria.

New and improved results for recurrent neural networks with interval time-varying delay

In this paper, the problem of stability analysis for a class of static recurrent neural networks with interval time-varying delay is considered. By constructing a newly augmented Lyapunov-Krasovskii functional containing triple integral terms and utilizing the inverses of first-order and squared reciprocally convex parameters techniques and zero equality, new and improved delay-dependent stability criteria are proposed to guarantee the asymptotic stability of the concerned networks with the framework of linear matrix inequalities (LMIs). Finally, some numerical examples are given to illustrate the effectiveness of the proposed methods.

Exponential synchronization of memristor-based neural networks with time-varying delay and stochastic perturbation

Abstract This paper deals with the stochastic exponential synchronization problem of memristor-based neural networks with time-varying delay. Firstly, considering the state-dependent properties of the memristor, less conservative of model is constructed to analyze the complicated memristor-based neural networks. Then, by applying the stochastic differential inclusions theory and Lyapunov functional approach, sufficient verifiable conditions that depend on the time-varying delay and stochastic perturbation are obtained. It is shown that synchronization can be realized by linear feedback control and adaptive feedback control. The derived results complement and improve the previously known results. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

Stochastic mean square exponential synchronisation of time-varying complex dynamical networks via pinning control

ABSTRACT This paper investigates the problem of stochastic mean square exponential synchronisation of complex dynamical networks with time-varying delay via pinning control. By applying the Lyapunov method and stochastic analysis, criteria on mean square exponential synchronisation are established under linear feedback pinning control and adaptive feedback pinning control, which depend on the time-varying delay and stochastic perturbation. These results complement and improve the previously known results. Two numerical examples are given to illustrate the effectiveness and correctness of the derived theoretical results.

Holistic adjustable delay interval method-based stability and generalized dissipativity analysis for delayed recurrent neural networks

Abstract This paper is concerned with the generalized dissipativity analysis for the recurrent neural networks (RNNs) with time-varying delays. The generalized dissipativity analysis contains a few previous known results, such as the passivity, [ τ j − 1 , τ j ] , -dissipativity, H∞ performance and j = 1 , … , p , performance in a unified framework. The delay interval with fixed terminals is changed into a dynamical one with adjustable delay interval based on convex combination technique (CCT), which is called adjustable delay interval method (ADIM). A novel augmented Lyapunov–Krasovskii functional (LKF) comprising triple integral terms and considering more information about neuron activation functions is constructed, in which the integral interval associated with delayed variables is not fixed. We give some sufficient conditions in terms of linear matrix inequalities (LMIs) to guarantee stability and generalized dissipativity of the considered neural networks. Finally, numerical examples are provided to demonstrate the effectiveness and less conservative of the obtained theoretical results.

Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays

This paper is concerned with exponential stability and extended dissipativity criteria for generalized discrete-time neural networks (GDNNs) with additive time-varying delays. The generalized dissipativity analysis combines a few previous results into a framework, such as l2−l∞ performance, H∞ performance, passivity performance, strictly (Q,S,R)−γ−dissipative and strictly (Q,S,R)−dissipative. The definition of exponential stability for GDNNs is given with a new and more appropriate expression. A novel augmented Lyapunov-Krasovskii functional (LKF) which involves more information about the additive time-varying delays is constructed. By introducing more zero equalities and using a new double summation inequality together with Finsler’s lemma, an improved delay-dependent exponential stability and extended dissipativity criterion are derived in terms of convex combination technique (CCT). Finally, numerical examples are given to illustrate the usefulness and advantages of the proposed methods.

Extended robust global exponential stability for uncertain switched memristor-based neural networks with time-varying delays

Abstract This paper is concerned with the problem of global exponential stability for uncertain memristive-based neural networks (UMNNs) with time-varying delays and switching parameters subject to unstable subsystems. Different from most of the existing papers, the considered uncertain switched MNNs with discrete-delays are modeled as switched neural networks (SNNs) with uncertain time-varying parameters. Based on multiple Lyapunov–Krasovskii functional (MLF) approach, average dwell time (ADT) technique and mode-dependent average dwell time (MDADT) method, some LMIs-based stability criteria are derived to design the switching signal and guarantee the exponential stability of the considered uncertain switched neural networks. By exploring the mode-dependent property of each subsystem, all the subsystems are categorized into stable and unstable ones. The concerned SNNs with both stable and unstable subsystems are more general and applicable than the existing models of SNNs only view all subsystems being stable, thus getting less conservatism criteria. The proposed sufficient conditions can be simplified into the forms of LMIs for conveniently using Matlab LMI toolbox. Finally, two numerical examples are exploited to demonstrate the effectiveness and applicability of the proposed theoretical results.

Lag synchronization analysis of general complex networks with multiple time-varying delays via pinning control strategy

This paper focuses on the lag synchronization issue for a kind of general complex networks with multiple time-varying delays via the pinning control strategy. By applying the Lyaponov functional theory and mathematical analysis techniques, sufficient verifiable criteria that depend on both intrinsic time-varying delay and coupled time-varying delay are obtained to achieve lag synchronization of the networks. Moreover, the coupling configuration matrices are not required to be symmetric or irreducible, and the minimum number of pinned nodes is determined by node dynamics, coupling matrices, and the designed parameter matrices. Finally, a numerical example is given to illustrate the feasibility of the theoretical results.