Sliding-mode {H_{infty}} synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays

Nannan Ma,Lin Chen,Zhibin Liu

doi:10.1186/s13662-019-1987-6

Nannan Ma, Lin Chen + Show 1 more

Open Access

https://doi.org/10.1186/s13662-019-1987-6

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Abstract

This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of an appropriate Lyapunov–Krasovskii functional, a set of new sufficient conditions is developed which not only guarantee the stochastic stability of the sliding-mode dynamics, but also satisfy the {H_{infty}} performance. Next, an integral sliding surface is designed to guarantee that the closed-loop error system reach the designed sliding surface in a finite time. Finally, an example is given to illustrate the validity of the obtained theoretical results.

Highlights

In recent years, increasing attention has been drawn to the problem of complex networks due to their potential applications in many real-world systems, such as biological systems, chemical systems, social systems and technological systems
The main contributions of this article are summarized as follows: (1) This paper extends previous work on the synchronization problem for complex dynamical network systems with Markovian jump parameters and time-varying delays and derives some new theoretical results
The following complex dynamical network systems of N identical nodes is considered, in which each node consists of an n-dimensional dynamical subsystem with Markovian jump parameter and time delay:

Summary

Introduction

In recent years, increasing attention has been drawn to the problem of complex networks due to their potential applications in many real-world systems, such as biological systems, chemical systems, social systems and technological systems. Based on sampled-data control [15], the authors proposed a method with finite-time H∞ synchronization in Markovian jump complex networks with timevarying delays. The goal is to select suitable sliding control to synchronize complex networks with Markovian jump parameters and time delays. To achieve the H∞ synchronization of complex dynamical networks with Markovian jump parameter, the integral sliding surface is designed, and a novel sliding-mode controllers is proposed. The main contributions of this article are summarized as follows: (1) This paper extends previous work on the synchronization problem for complex dynamical network systems with Markovian jump parameters and time-varying delays and derives some new theoretical results. The following complex dynamical network systems of N identical nodes is considered, in which each node consists of an n-dimensional dynamical subsystem with Markovian jump parameter and time delay:.

Or equivalently

And the outer coupling matrix is given as

Conclusion