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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: fuyanming@hit.edu.cn.
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: fuyanming@hit.edu.cn.
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: fuyanming@hit.edu.cn.
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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

References

[1]Benjelloun, K. and Boukas, E. K., “Stochastic stability of linear time-delay system with Markovian jumping parameters”, Math. Prob. Eng. 3 (1997) 187–201.CrossRefGoogle Scholar
[2]Boukas, E. K. and Liu, Z. K., “Output-feedback guaranteed cost control for uncertain time-delay systems with Markov jumps”, Proceedings of the American Control Conference 4 (2000) 2784–2788.Google Scholar
[3]Boukas, E. K. and Yang, H. “Stability of stochastic systems with jumps”, Math. Prob. Eng. 3 (1996) 173–185.CrossRefGoogle Scholar
[4]Cao, Y. Y. and Lam, J. “Robust H ∞ control of uncertain Markovian jump systems with time-delay”, IEEE Trans. Auto. Control 45 (2000) 77–85.Google Scholar
[5]Costa, O. L. and Marques, P. P., “Mix H2/H∞-control of discrete-time Markovian jump linear systems”, IEEE Trans. Auto. Control 43 (1998) 95–100.CrossRefGoogle Scholar
[6]Dai, L., Singular control systems (Springer, Berlin, 1989).CrossRefGoogle Scholar
[7]Duan, G. R. and Patton, R. J., “Eigenstructure assignment in descriptor systems via proportional plus derivative state feedback”, Int. J. Control 68 (1997) 1147–1162.CrossRefGoogle Scholar
[8]Farias, D. O. D., Geromel, J. C., Do, J. B. R. and Costa, O. L., “Output feedback control of Markov jump linear systems”, IEEE Trans. Auto. Control 45 (2000) 944–949.CrossRefGoogle Scholar
[9]Ji, Y. D. and Chizeck, H. J., “Stability, and continuous-time Markovian jump linear quadratic control”, IEEE Trans. Auto. Control 35 (1990) 777–788.CrossRefGoogle Scholar
[10]Li, X. and Souza, C. E., “Criteria for robust stability and stabilization of uncertain linear systems with state delay”, Automatica 33 (1999) 1657–1662.CrossRefGoogle Scholar
[11]Lu, C., Tsai, J., Jong, G. and Su, T. “An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays”, IEEE Trans. Auto. Control 48 (2003) 286–289.Google Scholar
[12]Mao, X. R., “Exponential stability of stochastic delay interval systems with Markovian switching”, IEEE Trans. on Automatic Control 47 (2002) 1604–1612.Google Scholar
[13]Mao, X. R., Koroleva, N. and Rodkina, A. “Robust stability of uncertain stochastic differential delay equations”, Syst. Control Lett. 35 (1998) 325–336.CrossRefGoogle Scholar
[14]Masubuchi, L., Kamitane, Y., Ohara, A. and Suda, N. “H ∞ control for descriptor systems: A matrix inequalities approach”, Automatica 33 (1997) 667–673.CrossRefGoogle Scholar
[15]Moheimani, S. O. R. and Petersen, I. R., “Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems”, IEE Proc. Control Theory Appl. 144 (1997) 183–188.CrossRefGoogle Scholar
[16]Nian, X. and Feng, J. “Guaranteed-cost control of a linear uncertainsystem with multiple time-varying delays: an LMI approach”, IEE Proc. Control Theory Appl. 150 (2003) 17–21.CrossRefGoogle Scholar
[17]Park, J. H., “Robust guaranteed cost for uncertain linear differential systems of neutral type”, Appl. Math. Comput. 140 (2003) 523–535.Google Scholar
[18]Lin, Z., Guan, X. and Duan, G. “Robust guaranteed cost control for discrete-time uncertain systems with delay”, IEE Proc. Control Theory Appl. 146 (1999) 428–432.Google Scholar
[19]Xu, S., Lam, J. and Zhang, L. “Robust D-stability analysis for uncertain discrete singular systems with state delays”, IEEE Trans. Circuits Syst. 49 (2002) 551–555.Google Scholar
[20]Xu, S. Y., Dooren, P. V., Stefan, R. and Lam, J. “Robust stability and stabilization for singular systems with state delay and parameter uncertainty”, IEEE Trans. Auto. Control 47 (2002) 1122–1128.Google Scholar
[21]Yu, L. and Chu, J. “An LMI approach to guaranteed cost control of linear uncertain time-delay systems”, Automatica 35 (1999) 1155–1159.CrossRefGoogle Scholar
[22]Yu, L. and Gao, F. R., “Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delay”, J. Franklin Inst. 338 (2001) 101–110.CrossRefGoogle Scholar
[23]Yue, D. and Lam, J. “Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying State and input delays”, Optimal Control Appl. Methods 26 (2005) 85–105.CrossRefGoogle Scholar
[24]Zhang, L., Huang, B. and Lam, J. “Robust guaranteed cost control of descriptor systems”, Dyn. Contin. Discrete Impuls. Syst. Ser. B 10 (2003) 633–646.Google Scholar