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DELAY-DEPENDENT ROBUST H∞ CONTROL FOR SINGULAR SYSTEMS WITH MULTIPLE DELAYS

Part of: Functional-differential and differential-difference equations Control systems

Published online by Cambridge University Press:  01 October 2008

SHUQIAN ZHU ,
CHENGHUI ZHANG ,
XINZHI LIU  and
ZHENBO LI
SHUQIAN ZHU
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, P. R. China (email: sqzhu@sdu.edu.cn)
CHENGHUI ZHANG
Affiliation:
School of Control Science and Engineering, Shandong University, Jinan 250061, P. R. China (email: zchui@sdu.edu.cn)
XINZHI LIU*
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (email: xzliu@uwaterloo.ca)
ZHENBO LI
Affiliation:
School of Statistics and Mathematics, Shandong Economic University, Jinan 250014, P. R. China (email: lizhenbo@126.com)
*
✉For correspondence; e-mail: xzliu@uwaterloo.ca
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Abstract

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This paper studies the problem of delay-dependent robust H∞ control for singular systems with multiple delays. Based on a Lyapunov–Krasovskii functional approach, an improved delay-dependent bounded real lemma (BRL) for singular time-delay systems is established without using any of the model transformations and bounding techniques on the cross product terms. Then, by applying the obtained BRL, a delay-dependent condition for the existence of a robust state feedback controller, which guarantees that the closed-loop system is regular, impulse free, robustly stable and satisfies a prescribed H∞ performance index, is proposed in terms of a nonlinear matrix inequality. The explicit expression for the H∞ controller is designed by using linear matrix inequalities and the cone complementarity iterative linearization algorithm. Numerical examples are also given to illustrate the effectiveness of the proposed method.

Keywords

singular time-delay systemmultiple delaysdelay-dependent robust H∞ controlbounded real lemmalinear matrix inequality

MSC classification

Secondary: 93C15: Systems governed by ordinary differential equations 34K06: Linear functional-differential equations 34K20: Stability theory
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 2 , October 2008 , pp. 209 - 230
Copyright
Copyright © Australian Mathematical Society 2009

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