Stabilization of complex network with hybrid impulsive and switching control

This paper studies the asymptotic stability properties of a class of complex dynamical networks under a hybrid impulsive and switching control. By utilizing the concept of impulsive control and the stability results for impulsive systems, some new criteria for global and local stability are established for this model. Some numerical examples and simulations are included to illustrate the effectiveness of the theoretical results.     

Synchronization of delayed complex dynamical networks with impulsive and stochastic effects

In this paper, the globally exponential synchronization of delayed complex dynamical networks with impulsive and stochastic perturbations is studied. The concept named “average impulsive interval” with “elasticity number” of impulsive sequence is introduced to get a less conservative synchronization criterion. By comparing with existing results, in which maximum or minimum of impulsive intervals are used to derive the synchronization criterion, the proposed synchronization criterion increases (or decreases) the impulse distances, which leads to the reduction of the control cost (or enhance the robustness of anti-interference) as the most important characteristic of impulsive synchronization techniques. It is discovered in our criterion that “elasticity number” has influence on synchronization of delayed complex dynamical networks but has no influence on that of non-delayed complex dynamical networks. Numerical simulations including a small-world network coupled with delayed Chua’s circuit are given to show the effectiveness and less conservativeness of the theoretical results.     

Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations

In this paper, we study the exponential synchronization problem of a class of chaotic delayed neural networks with impulsive and stochastic perturbations. The involved time delays include time-varying delays and unbounded distributed delays. Employing the method of impulsive delay differential inequality, several new sufficient conditions ensuring the exponential synchronization are obtained, which can be easily checked by LMI Control Toolbox in Matlab. Compared with the previous methods, our method does not resort to complicated Lyapunov–Krasovkii, and the results derived are independent of the time-varying delays and do not require the differentiability of delay functions and the monotony of the activation functions. Finally, a numerical example and its simulation is given to show the effectiveness of the obtained results in this paper.     

Synchronization of delayed fuzzy cellular neural networks with impulsive effects

This letter studies synchronization of delayed fuzzy cellular neural networks with impulses and all the parameters unknown. To avoid the difficulties which may be brought by the impulses, a non-impulsive system is used to replaced the system with impulses. Then by the well known Lyapunov–Lasall principle, some new stability criteria are obtained. An example and its simulation were given to illustrate the simpleness and effectiveness of our main results.     

Stability analysis of impulsive parabolic complex networks

In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.     

Neural network hybrid adaptive control for nonlinear uncertain impulsive dynamical systems

A neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach.     

Synchronization of switched neural networks with mixed delays via impulsive control

This paper concerns the problem of global exponential synchronization for a class of switched neural networks with time-varying delays and unbounded distributed delays via impulsive control method. By using Lyapunov stability theory, new synchronization criterion is derived. In our synchronization criterion, the switching law can be arbitrary and the concept of average impulsive interval is utilized such that the obtained synchronization criterion is less conservative than those based on maximum of impulsive intervals. Numerical simulations are given to show the effectiveness and less conservativeness of the theoretical results.     

Stability of random impulsive coupled systems on networks with Markovian switching

Abstract

This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dynamics are stable while impulses are unstable; (2) impulses are stable while continuous dynamics are unstable. To begin with, based on Lyapunov method as well as graph-theoretic technique, several new stability criteria in two cases are derived, that are, the Lyapunov-type criteria and the coefficients-type criteria. Then main results are used for a class of random impulsive coupled oscillators. Finally, the effectiveness of the obtained results is verified by numerical simulations.     

Synchronization of master-slave markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin's formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.     

Multistability in impulsive hybrid Hopfield neural networks with distributed delays

In this paper we investigate multistability of Hopfield-type neural networks with distributed delays and impulses, by using Lyapunov functionals, stability theory and control by impulses. Example and simulation results are given to illustrate the effectiveness of the results.     

Multiple periodic solutions in impulsive hybrid neural networks with delays

The existence of multiple periodic solutions and their exponential stability are investigated for impulsive hybrid Hopfield-type neural networks with both time-dependent and distributed delays, using the Leray-Schauder fixed point theorem and Lyapunov functionals. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses, providing flexibility for the analysis and design of delayed neural networks with impulse effects. Examples are given.     

Towards hybrid system modeling of uncertain complex dynamical systems

In this paper we consider the problem of finding a low dimensional approximate model for a discrete time Markov process. This problem is of particular interest in systems that exhibit so-called metastable behavior, i.e. systems whose behavior is principally concentrated on a finite number of disjoint components of the state space. The approach developed here is based on a proper orthogonal decomposition and, unlike most existing approaches, does not require the Markov chain to be reversible. An example is presented to illustrate the effectiveness of the proposed method.     

Stability and stabilization of impulsive switched system with inappropriate impulsive switching signals under asynchronous switching

The main objective of this paper is to study the stability and stabilization problems for a class of impulsive switched systems with inappropriate impulsive switching signals under asynchronous switching. Here, “inappropriate” means that the impulse jump moment may be inconsistent with the asynchronous switching moment or the system switching moment. And “asynchronous” implies that the switching of controller modes lags behind that of system modes. The hybrid case of stable or unstable subsystems combining with stable and unstable impulses is explored. A novel Lyapunov-like function is constructed, which is discontinuous at some special instants, including the switching instants, the instants when the system modes and filter modes are matched, and the impulse jump instants. Based on the novel multiple Lyapunov-like function, the sufficient conditions for the closed loop system to be globally uniformly exponentially stable (GUES) are obtained with admissible edge-dependent switching signals. Furthermore, by excogitating the state-feedback switching controller, the gain matrix of the controller can be obtained by solving the linear matrix inequalities. Finally, two numerical examples and simulation results are given to prove the effectiveness of our main results.     

Synchronization in complex networks with distinct chaotic nodes

We present an approach to the chaos synchronization of complex networks with distinct nodes. The chaotic synchronization is achieved by adding a derivative coupling term in the network equation. We assume that node in networks are different and are given by the Lorenz, Rössler, Chen and Sprott chaotic systems. The derivative term is capable to induce the synchronous behavior in the network. Moreover such a coupling leads the global behavior to a chaotic attractor. We found that without derivative coupling the network is leaded only to an equilibrium point or a limit cycle. Numerical simulations are provided to illustrate the result. Complementary the network synchrony can be chaotic in presence of the derivative coupling.     

Synchronization of singular complex dynamical networks with time-varying delays

This paper considers delay dependent synchronizations of singular complex dynamical networks with time-varying delays. A modified Lyapunov-Krasovskii functional is used to derive a sufficient condition for synchronization in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Numerical examples show the effectiveness of the proposed method.     

Parameter estimation and topology identification of uncertain fractional order complex networks

This paper focuses on a significant issue in the research of fractional order complex network, i.e., the identification problem of unknown system parameters and network topologies in uncertain complex networks with fractional-order node dynamics. Based on the stability analysis of fractional order systems and the adaptive control method, we propose a novel and general approach to address this challenge. The theoretical results in this paper have generalized the synchronization-based identification method that has been reported in several literatures on identifying integer order complex networks. We further derive the sufficient condition that ensures successful network identification. An uncertain complex network with four fractional-order Lorenz systems is employed to verify the effectiveness of the proposed approach. The numerical results show that this approach is applicable for online monitoring of the static or changing network topology. In addition, we present a discussion to explore which factor would influence the identification process. Certain interesting conclusions from the discussion are obtained, which reveal that large coupling strengths and small fractional orders are both harmful for a successful identification.     

Synchronization for a class of complex dynamical networks with time-delay

In this study, the synchronization problem is addressed for a class of complex dynamical networks in which every identical node is a time-delayed Lur’e system. Delay-dependent and delay-independent synchronization criteria are established through a decoupling technique, which reduces a group of high-dimensional linear matrix inequalities (LMIs) to the test of two groups of lower-dimensional LMIs. An extension to the synchronization of discrete-time Lur’e networks with time delay is also studied. The efficiency and applicability of the proposed methodology is demonstrated by a numerical example through simulation.     

Robust stability of uncertain impulsive dynamical systems

This paper studies robust stability of uncertain impulsive dynamical systems. By introducing the concepts of uniformly positive definite matrix functions and Hamilton–Jacobi/Riccati inequalities, several criteria on robust stability, robust asymptotic stability and robust exponential stability are established. An example is also worked through to illustrate our results.     

Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes

This paper studies the pinning impulsive synchronization problem for a class of complex dynamical networks with time-varying delay. By applying the Lyapunov stability theory and mathematical analysis technique, sufficient verifiable criterion for the synchronization of delayed complex dynamical networks with small delay is derived analytically. It is shown that synchronization can be achieved by only impulsively controlling a small fraction of network nodes. Moreover, a novel sufficient condition is constructed to relax the restrictions on the size of time-delay and guarantee the synchronization of concerned networks with large delay. Two numerical examples are presented to illustrate the effectiveness of the obtained results.     

Synchronization criterions and pinning control of general complex networks with time delay

The problems of synchronization and pinning control for general time-delay complex dynamical networks are investigated. In this paper, less conservative criterions for both continuous-time and discrete-time complex dynamical networks with time delay are obtained. Pinning control strategies are respectively, designed to make these complex dynamical networks synchronized. Moreover, the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities, which reduces the computation complexity. Finally, numerical simulations verify the effectiveness of our methodology.