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

Published online by Cambridge University Press:  17 February 2009

Yan-Ming Fu ,
Di Wu  and
Guang-Ren Duan
Yan-Ming Fu
Affiliation:
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P. O. Box 416, Harbin, 150001, P. R. China; e-mail: [email protected].
Di Wu
Affiliation:
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P. O. Box 416, Harbin, 150001, P. R. China; e-mail: [email protected].
Guang-Ren Duan
Affiliation:
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P. O. Box 416, Harbin, 150001, P. R. China; e-mail: [email protected].
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Abstract

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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.

Keywords

stochastic systemsdescriptor systemsMarkov processesguaranteed cost controllinear matrix inequalitiestime-delay systems.
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 4 , April 2006 , pp. 569 - 580
Copyright
Copyright © Australian Mathematical Society 2006

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