Synchronization Control for Neutral Stochastic Delay Markov Networks via Single Pinning Impulsive Strategy

This paper considers the problems on the mean square exponential synchronization and the almost surely exponential synchronization for neutral stochastic dynamical delay networks with Markovian switching via the single pinning impulsive control. By using a unified approach incorporating the concept of average impulsive interval and Lyapunov function, and the Borel-Cantelli lemma, two criteria on the mean square exponential stability and the almost surely exponential stability for impulsive neutral stochastic delay systems with Markovian switching are derived. It is shown that the impulsive control with a suitable impulsive strength can stochastically stabilize the underlying systems. With the symmetry and irreducibility of the switching topologies, and the obtained stochastic stability criteria, sufficient conditions are derived to determine the mean square exponential synchronization of the underlaying networks via the single pinning impulsive controller, which are given with algebraic inequalities and M -matrix. The almost surely exponential synchronization is also analyzed. Two examples are given to verify the validity of the theoretic results presented.

I. Introduction

Neutral delay systems (NDSs) is a class of differential difference equation [1], in which the time delay presented in the derivative of system state is referred to as the neutral time delay. Motivated by their applications in chemical process, the theory of aeroelasticity, classical mechanics, and Lotka–Volterra systems, many studies, see [2], [3] and the references therein, have considered the stability analysis of NDSs. When these systems are subject to environmental disturbances, their dynamical behavior can be characterized by neutral stochastic delay systems (NSDSs) [4]. Stochastic stability and some important control problems for NSDSs have been extensively investigated over past few years, (see [5], [6]). If the systems’ structure and parameters in the NSDSs experience abrupt changes described by the continuous-time Markov chains [8], NSDSs with Markovian switching have been proposed [8]. Some novel works about the stability analysis of stochastic differential equations with Markovian switching and NDSs with Markovian switching were given in [9], [10] and the references therein. Recently, stochastic stability and synthesis analysis of NSDSs with Markovian switching have been considered in [8], [11], [12], and the references therein.