RobustH∞Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach

Li-Li Liu,Yue-E Wang,Bao-Wei Wu

doi:10.1155/2014/790521

Abstract

A new version of delay-dependent bounded real lemma for singular systems with state delay is established by parameterized Lyapunov-Krasovskii functional approach. In order to avoid generating nonconvex problem formulations in control design, a strategy that introduces slack matrices and decouples the system matrices from the Lyapunov-Krasovskii parameter matrices is used. Examples are provided to demonstrate that the results in this paper are less conservative than the existing corresponding ones in the literature.

Highlights

During the last decade, a considerable amount of attention has been paid to stability and control of singular systems with delay, since they can better describe and analyze physical systems than the state-space time-delay ones [1, 2]
The problem of H∞ control for singular systems with delay has been investigated by many researchers and various approaches have been adopted [3,4,5,6,7,8,9,10,11,12,13,14,15]
One is the H∞ performance index while the other is admissible upper bound of the delay

Summary

Introduction

A considerable amount of attention has been paid to stability and control of singular systems with delay, since they can better describe and analyze physical systems than the state-space time-delay ones [1, 2]. The problem of H∞ control for singular systems with delay has been investigated by many researchers and various approaches have been adopted [3,4,5,6,7,8,9,10,11,12,13,14,15]. One is the H∞ performance index while the other is admissible upper bound of the delay. For a given time-delay, the smaller the H∞ performance index, the better the conditions; for a prescribed H∞ performance level, the larger the admissible upper bound of the time-delay, the less conservative the conditions

Objectives

Results

Conclusion