Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling

Rathinasamy Sakthivel,Chao Wang,Ramalingam Sakthivel,Yong-Ki Ma,Boomipalagan Kaviarasan

doi:10.1155/2018/8546304

Abstract

The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

Highlights

During the past twenty years, the investigation of complex dynamical networks (CDNs) that consist of a huge number of interacting dynamical nodes has received a great deal of attention from various science and engineering areas, such as social networks, ecological prey-predator networks, protein networks, power grids, and ecosystems [1, 2]
Motivated by the above analysis, in this paper, we focus on the finite-time nonfragile synchronization problem is investigated for a class of CDNs subject to semi-Markov jump topology and stochastic noises
Based on the Lyapunov-Krasovskii stability theory, this section aims to develop a new set of delay-dependent sufficient conditions that can guarantee the stochastic synchronization of the considered network model (1) over a finite-time interval

Summary

Introduction

During the past twenty years, the investigation of complex dynamical networks (CDNs) that consist of a huge number of interacting dynamical nodes has received a great deal of attention from various science and engineering areas, such as social networks, ecological prey-predator networks, protein networks, power grids, and ecosystems [1, 2]. Synchronization phenomenon is the most important behavior and several interesting and efficient methodologies have been developed in the literature to solve the synchronization problem of various kinds of CDNs; for instance, see [3,4,5,6,7]. It is worth mentioning that the CDN representing real-time systems is generally affected by external noise factors or stochastic disturbances [8]. The consideration of external noise factors in the study of synchronization of CDNs is of great importance in the viewpoints of both theoretical and practical.

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