H∞ Control for Stochastic Singular Systems With Time-Varying Delays

Shuangyun Xing,Xishun Yue,Meng Wang

doi:10.1109/access.2020.3021009

Shuangyun Xing, Xishun Yue + Show 1 more

Open Access

https://doi.org/10.1109/access.2020.3021009

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Abstract

In this article, we study the H ∞ control problems for stochastic singular systems with time-varying delays. Firstly, a new Lyapunov-Krasovskii functional is constructed, employing the free weighting matrix technique and Jensen inequality, the stochastic admissibility criteria in the mean square for stochastic singular time-varying delay systems are proposed on the basis of the auxiliary vector function. Secondly, the state feedback controller is designed such that the resulting closed-loop system meets regular, impulse-free, stochastically stable in the mean square and has H ∞ performance γ. In the proof process, the dual equation is used to derive the conditions of stochastic admissibility in the mean square. Finally, a practical example of DC motor model is presented to show the validity of our proposed theoretical results.

Highlights

In the past few decades, singular systems play an important role in many scientific fields, such as biologic systems, circuit systems and power systems
We focus on studying the H∞ control problem for stochastic singular systems with time-varying delays
The main contributions of this study include: 1) We study the stability and H∞ control for singular systems with time-varying delays and stochastic disturbances at the same time

Summary

INTRODUCTION

In the past few decades, singular systems play an important role in many scientific fields, such as biologic systems, circuit systems and power systems. Xia et al [27] studied about the problem of filtering for nonlinear singular Markovian jumping systems with interval time-varying delays. It increases the difficulty of stability and related control analysis of the systems when the singular systems have both time-varying delays and random disturbance, and gradually attracts more and more attention. Li et al [29] studied stability and stabilisation problems for a series of continuous stochastic singular systems with multiple time-varying delays via a delay-distribution-dependent Lyapunov functional, and so on. We focus on studying the H∞ control problem for stochastic singular systems with time-varying delays. If the dimensions of matrices are not explicitly specified, they are assumed to be algebraically compatible

PROBLEM FORMULATION AND PRELIMINARIES

TATd X TATd

TBv 0 X T 0

CONCLUSION