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Non-fragile \(H_\infty \) filter design for linear continuous-time systems. (English) Zbl 1152.93365

Summary: This paper studies the problem of non-fragile \(H_\infty \) filter design for linear continuous-time systems. The filter to be designed is assumed to include additive gain variations, which result from filter implementations. A notion of structured vertex separator is proposed to approach the problem, and exploited to develop sufficient conditions for the non-fragile \(H_\infty \) filter design in terms of solutions to a set of Linear Matrix Inequalities (LMIs). The designs guarantee the asymptotic stability of the estimation errors, and the \(H_\infty \) performance of the system from the exogenous signals to the estimation errors below a prescribed level. A numerical example is given to illustrate the effect of the proposed method.

MSC:

93B36 \(H^\infty\)-control
93C05 Linear systems in control theory
93D20 Asymptotic stability in control theory
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[1] Dorato, P., Non-fragile controller design, an overview, Proceedings of American Control Conference, 5, 2829-2831 (1998)
[2] Famularo, D.; Dorato, P.; Abdallah, C. T.; Haddad, W. M.; Jadbabais, A., Robust non-fragile LQ controllers: The static state feedback case, International Journal of Control, 73, 2, 159-165 (2000) · Zbl 1006.93514
[3] Fu, M.; de Souza, C. E.; Xie, L., \(H_\infty\) estimation for uncertain systems, International Journal of Robust Nonlinear Control, 2, 87-105 (1992) · Zbl 0765.93032
[4] Gao, H. J.; Lam, J.; Wang, C. H., Induced \(L_2\) and generalized \(H_2\) filtering for systems with repeated scalar nonlinearities, IEEE Transactions on Signal Processing, 53, 11, 4215-4226 (2005) · Zbl 1370.94125
[5] Geromel, J. C.; de Oliviera, M. C., \(H_2\) and \(H_\infty\) robust filtering for convex bounded uncertain systems, IEEE Transactions on Automatic Control, 46, 1, 100-107 (2001)
[6] Haddad, W. M.; Corrado, J. R., Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations, International Journal of Control, 73, 15, 1405-1423 (2000) · Zbl 1062.93503
[7] Ho, M.-T.; Datta, A.; Bhatacharyya, S. P., Robust and non-fragile PID controller design, International Journal of Robust and Nonlinear Control, 11, 7, 681-708 (2001) · Zbl 0993.93009
[8] Iwasaki, T.; Shibata, G., LPV system analysis via quadratic separator for uncertain implicit systems, IEEE Transactions on Automatic Control, 46, 1195-1208 (2001) · Zbl 1006.93053
[9] Jadbabaie, A.; Abdallah, C. T.; Famularo, D.; Dorato, P., Robust, non-fragile and optimal controller design via linear matrix inequalities, Proceedings of American Control Conference, 5, 2842-2846 (1998)
[10] Keel, L. H.; Bhatacharyya, S. P., Robust, fragile, or optimal?, IEEE Transactions on Automatic Control, 42, 8, 1098-1105 (1997) · Zbl 0900.93075
[11] Li, H.; Fu, M., A linear matrix inequality approach to robust \(H_\infty\) filtering, IEEE Transaction on Signal processing, 45, 2338-2350 (1997)
[12] Li, G., On the structure of digital controller with finite word length consideration, IEEE Transaction on Automatic Control, 43, 689-693 (1998) · Zbl 0989.93535
[13] Mahmoud, M. S., Resilient linear filtering of uncertain systems, Automatica, 40, 1797-1802 (2004) · Zbl 1162.93403
[14] Mahmoud, M. S., Resilient \(L_2 - L_1\) filtering of polytopic systems with state delays, IET Control Theory and Applications, 1, 1, 141-154 (2007)
[15] Nagpal, K. M.; Khargonekar, P. P., Filtering and smoothing in an \(H_\infty\) setting, IEEE Transaction on Automatic Control, 36, 2, 152-166 (1991) · Zbl 0758.93074
[16] De Oliveira, M. C.; Geromel, J. C., \(H_2\) and \(H_\infty\) filtering design subject to implementation uncertainty, SIAM Journal on Control and Optimization, 44, 2, 515-530 (2006) · Zbl 1210.93076
[17] Palhares, R. M.; Peres, P. L.D., Robust \(H_\infty\) filtering design with pole placement constraint via LMIs, Journal of Optimization Theory and Applications, 102, 2, 239-261 (1999) · Zbl 0941.93018
[18] Petersen, I. R., A stabilization algorithm for a class of uncertain linear systems, System & Control Letters, 8, 5, 351-357 (1987) · Zbl 0618.93056
[19] Peaucelle, D., Arzelier, D., & Farges, C. (2004). LMI results for resilient state-feedback with \(H_\infty \)Proceedings of the 43th IEEE conference on decision and control; Peaucelle, D., Arzelier, D., & Farges, C. (2004). LMI results for resilient state-feedback with \(H_\infty \)Proceedings of the 43th IEEE conference on decision and control
[20] Scherer, C. W. (1997). A full block S-procedure with applications. In Proceedings of the 36th IEEE conference on decision and control; Scherer, C. W. (1997). A full block S-procedure with applications. In Proceedings of the 36th IEEE conference on decision and control
[21] Takahashi, R. H. C., Dutra, D. A., Palhares, R. M., Peres, P. L. D. (2000). On robust non-fragile static state-feedback controller synthesis. In Proceedings of the 39th IEEE conference on decision and control,; Takahashi, R. H. C., Dutra, D. A., Palhares, R. M., Peres, P. L. D. (2000). On robust non-fragile static state-feedback controller synthesis. In Proceedings of the 39th IEEE conference on decision and control,
[22] Yang, G.-H.; Wang, J. L.; Lin, C., Non-fragile \(H_\infty\) control for linear systems with additive controller gain variations, International Journal of Control, 73, 16, 1500-1506 (2000) · Zbl 1009.93020
[23] Yang, G.-H.; Wang, J. L., Robust nonfragile Kalman filtering for uncertain linear systems with estimation gain uncertainty, IEEE Transaction on Automatic Control, 46, 2, 343-348 (2001) · Zbl 1056.93635
[24] Yang, G.-H.; Wang, J. L., Non-fragile \(H_\infty\) control for linear systems with multiplicative controller gain variations, Automatica, 37, 5, 727-737 (2001) · Zbl 0990.93031
[25] Yang, G.-H.; Wang, J. L., Non-fragile \(H_\infty\) output feedback controller design for linear systems, Journal of Dynamic Systems Measurement and Control Transactions of the ASME, 125, 1, 117-123 (2003)
[26] Yaz, E. E.; Jeong, C. S.; Yaz, Y. I., An LMI approach to discrete-time observer design with stochastic resilience, Journal of Computational and Applied Mathematics, 188, 2, 246-255 (2006) · Zbl 1108.93026
[27] Yaesh, I.; Shaked, U., Game theory approach to optimal linear estimation in the minimum \(H_\infty\) norm sense, IEEE Transaction on Automatic Control, 37, 6, 828-831 (1992) · Zbl 0769.90087
[28] Zhou, K.; Doyle, J. C.; Glover, K., Robust and optimal control (1996), Prentice Hall: Prentice Hall New Jersey · Zbl 0999.49500
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