ANZIAM  J.  47 (2006), 569-580

Robust guaranteed cost control for descriptor systems with Markov jumping parameters and state delays

Yan-Ming Fu   Center for Control Theory and   Guidance Technology   Harbin Institute of Technology   P. O. Box 416   Harbin 150001   P. R. China     fuyanming@hit.edu.cn Di Wu   Center for Control Theory and   Guidance Technology   Harbin Institute of Technology   P. O. Box 416   Harbin 150001   P. R. China     and Guang-Ren Duan   Center for Control Theory and   Guidance Technology   Harbin Institute of Technology   P. O. Box 416   Harbin 150001   P. R. China

Abstract

This paper deals with robust guaranteed cost control for a class of linear uncertain descriptor systems with state delays and jumping parameters. The transition of the jumping parameters in the systems is governed by a finite-state Markov process. Based on stability theory for stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost controllers is derived. In terms of the LMI (linear matrix inequality) approach, a linear state feedback controller is designed to stochastically stabilise the given system with a cost function constraint. A convex optimisation problem with LMI constraints is formulated to design the suboptimal guaranteed cost controller. A numerical example demonstrates the effect of the proposed design approach.

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