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Guaranteed Cost Control for Discrete-time Linear Uncertain Systems with Time-varying Delay  

Kim, Ki-Tae (School of and Electrical Engineering, and Computer Science Kyungpook National University)
Cho, Sang-Hyun (School of and Electrical Engineering, and Computer Science Kyungpook National University)
Lee, Sang-Kyung (Department of Automation Systems, Doowon Technical College)
Park, Hong-Bae (School of and Electrical Engineering, and Computer Science Kyungpook National University)
Publication Information
Journal of the Institute of Electronics Engineers of Korea SC / v.39, no.6, 2002 , pp. 20-26 More about this Journal
Abstract
This paper deals with the guaranteed cost control problems for a class of discrete-time linear uncertain systems with time-varying delay. The uncertain systems under consideration depend on time-varying norm-bounded parameter uncertainties. We address the existence condition and the design method of the memoryless state feedback control law such that the closed loop system not only is quadratically stable but also guarantees an adequate level of performance for all admissible uncertainties. Through some changes of variables and Schur complement, It is shown that the sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.
Keywords
Guaranteed cost control; discrete-time linear uncertain system; time-varying delay; linear matrix inequality;
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1 X. Li and C. E. Souza, 'Criteria for robust stability and stabilization of uncertain linear systems with time-delay,' Automatica, vol. 33, pp. 1657-1662, 1997   DOI   ScienceOn
2 S. O. R. Moheimani and I. R. Petersen, 'Optimal quadratic guaranteed cost control of a class of uncertain time delay systems,' IEE Proc., Control Theory Appl., vol. 144, no. 2, pp. 183-188, Mar. 1997   DOI   ScienceOn
3 S. H. Song, J. K. Kim, C. H. Yim, and H. C. Kim, '$H_{\infty}$ control of discrete-time linear systems with time-varying delays in state,' Automatica, vol. 35, pp. 1587-1591, 1999   DOI   ScienceOn
4 L. Yu, F. Gao, and A. Xue, 'Guaranteed cost control of uncertain discrete linear time-delay systems,' Proceeding of the American Control Conference, pp. 2481-2485, Chicago, Illinois, June 2000   DOI
5 I. R. Petersen, 'A stabilization algorithm for a class of uncertain linear systems,' Syst. Cont. Lett. vol. 8, pp. 351-357, 1987   DOI   ScienceOn
6 L. Yu, 'Guaranteed cost control of uncertain linear discrete-time systems,' Proceeding of the American Control Conference, pp. 3181-3184, Albuquerque, New Mexico, June 1997   DOI
7 J. Wang, L. Yu, H. Su, and J. Chu, 'Guaranteed cost output control of linear time-varying uncertain discrete systems,' Proceedings of the 36th Conference on Decision & Control, San Diego, California, USA, Dec. 1997   DOI
8 S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix Inequalities in System and Control Theory, SIAM, 1994
9 S. H. Esfahani, S. O. R. Moheimani, and I. R. Petersen, 'LMI approach to suboptimal guaran teed cost control for uncertain time-delay systems,' IEE Proc., Control Theory Appl., vol. 145, no. 6, pp. 491-498, Nov. 1998   DOI   ScienceOn
10 X. Guan, Z. Lin, and G. Duan, 'Robust guaranteed cost control for discrete-time uncertain systems with delay,' IEE Proc., Control Theory Appl., vol. 146, no. 6, pp. 598-602, Nov 1999   DOI   ScienceOn
11 J. Hennet and S. Tarbouriech, 'Stability and stabilization of delay differential systems,' Automatica, vol. 33, pp. 347-354, 1997   DOI   ScienceOn
12 E. T. Jeung, D. C. Oh, J. H. Kim, and H. B. park, 'Robust controller design for uncertain systems with time delays : LMI approach,' Automatica, vol. 32, pp. 1229-1231, 1996   DOI   ScienceOn
13 H. Kokame, H. Kobayashi, and T. Mori, 'Robust $H_{\infty}$ performance for linear delay-differential systems with time-varying uncertainties,' IEEE Trans. Automat. Contr., vol. 43, no. 2, pp. 223-226, Feb. 1998   DOI   ScienceOn