Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay

Tengyu Ma,Longsuo Li

doi:10.1186/s13660-018-1886-5

Abstract

This work mainly studies the robust stability analysis and design of a controller for uncertain neutral stochastic nonlinear systems with time-delay. Using a modified Lyapunov–Krasovskii functional and the free-weighting matrices technique, we establish some new delay-dependent criteria in terms of linear matrix inequality (LMI). The innovative point of this work is that we generalize the robust stability analysis of nonlinear stochastic time-delay systems to the uncertain neutral stochastic systems. Due to the added derivative term of time-delay, the proposed scheme can be applied more widely. Finally, numerical examples are provided to validate the derived results.

Highlights

Time-delay systems are widely used to model concrete systems in engineering sciences, such as biology, chemistry, mechanics [1–3]
Considerable attention has been devoted to stochastic systems governed by Itô stochastic differential equations, where the noises are described by Brownian motion [15, 16]
The neutral stochastic systems can effectively model a class of physical dynamical systems, since the mathematical models of them include the time-delays of state and its derivative

Summary

Introduction

Time-delay systems are widely used to model concrete systems in engineering sciences, such as biology, chemistry, mechanics [1–3]. Wang et al in [19] considered the problems of non-fragile robust stochastic stabilization and robust H∞ control for uncertain stochastic nonlinear time-delay systems. The neutral stochastic systems can effectively model a class of physical dynamical systems, since the mathematical models of them include the time-delays of state and its derivative These models have received considerable attention recently [21–25]. The authors in [33] constructed a new sliding surface functional and considered the H∞ sliding mode control (SMC) for uncertain neutral stochastic systems with Markovian jumping parameters and time-varying delays. Inspired by the above works, we investigate the robust stability of neutral stochastic time-delay nonlinear systems with one-sided Lipschitz condition. 4, we give two delay-dependent sufficient conditions for uncertain neutral stochastic nonlinear time-delay systems. The procedure of replacing (1) by (2) is called the S-procedure

Problem formulation

E1T –τ –1R–1

Conclusions