×

Robust \(H_{\infty}\) filtering with error variance constraints for discrete time-varying systems with uncertainty. (English) Zbl 1022.93046

The problem of robust \(H_\infty\)-filtering over a finite horizon is considered for discrete time-varying systems subject to unmeasured parameter perturbations in both the state and the output matrices of the state-space model. Sufficient conditions for the finite-horizon filter to satisfy state estimation error variance constraints as well as a prescribed \(H_\infty\)-performance for all admissible perturbations are given in terms of two unilaterally coupled discrete Riccati difference equations. The Riccati difference equations can be implemented for recursive computation in online applications. The results for time-varying systems has been extended to cover the case of stationary filtering over an infinite horizon for time-invariant systems. An example for estimating an inaccessible output of a time-varying uncertain system has been provided to illustrate how the special free parameter can be exploited to ensure that the bounds on the state estimation error variances stay below prescribed levels.

MSC:

93E11 Filtering in stochastic control theory
93C55 Discrete-time control/observation systems
93B36 \(H^\infty\)-control
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson, B. D.O.; Moore, J. B., Optimal filtering (1979), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0758.93070
[2] Bernstein, D. S.; Haddad, W. M., Steady-state Kalman filtering with an \(H_∞\) error bounded, Systems & Control Letters, 12, 9-16 (1989) · Zbl 0684.93081
[3] Bolzen, P.; Maroni, M., New conditions for the convergence of \(H_∞\) filters and predictors, IEEE Transactions on Automatic Control, 44, 1564-1568 (1999) · Zbl 0955.93053
[4] de Souza, C. E.; Fu, M.; Xie, L., \(H_∞\) analysis and synthesis of discrete-time systems with time-varying uncertainty, IEEE Transactions on Automatic Control, 38, 459-462 (1993) · Zbl 0791.93064
[5] de Souza, C. E.; Shaked, U.; Fu, M., Robust \(H_∞\) filtering for continuous time varying uncertain systems with deterministic input signals, IEEE Transactions on Signal Processing, 43, 709-719 (1995)
[6] de Souza, C. E.; Xie, L., Robust \(H_∞\) filtering, Control & Dynamic Systems, 65, 323-377 (1994) · Zbl 0817.93069
[7] Fu, M.; de Souza, C. E.; Xie, L., \(H_∞\) estimation for uncertain systems, International Journal of Robust Nonlinear Control, 2, 87-105 (1992) · Zbl 0765.93032
[8] Green, M.; Limebeer, D. J.N., Linear robust control (1994), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[9] Kwakernaak, H.; Sivan, R., Linear optimal control systems (1972), Wiley: Wiley New York · Zbl 0276.93001
[10] Li, H., & Fu, M. (1995). An LMI approach to robust \(H_∞\)Proceedings of IEEE conference on decision and control; Li, H., & Fu, M. (1995). An LMI approach to robust \(H_∞\)Proceedings of IEEE conference on decision and control
[11] Mangoubi, R. S., Appleby, B. D., & Verghese, G. C. (1994). Robust estimation for discrete-time linear systems. Proceedings of American control conference; Mangoubi, R. S., Appleby, B. D., & Verghese, G. C. (1994). Robust estimation for discrete-time linear systems. Proceedings of American control conference
[12] Packard, A.; Doyle, J. C., Quadratic stability with real and complex perturbations, IEEE Transactions on Automatic Control, 35, 198-201 (1990) · Zbl 0705.93060
[13] Petersen, I. R., & McFarlane, D. C. (1991). Robust state estimation for uncertain systems. Proceedings of IEEE conference on decision and control; Petersen, I. R., & McFarlane, D. C. (1991). Robust state estimation for uncertain systems. Proceedings of IEEE conference on decision and control
[14] Rawson, J. L., & Hsu, C. S. (1997). Reduced order \(H_∞\)Proceedings of IEEE conference on decision and control; Rawson, J. L., & Hsu, C. S. (1997). Reduced order \(H_∞\)Proceedings of IEEE conference on decision and control
[15] Shaked, U.; de Souza, C. E., Robust minimum variance filtering, IEEE Transactions on Signal Processing, 43, 2474-2483 (1995)
[16] Shaked, U., & Theodor, Y. (1992). \(H_∞\)Proceedings of IEEE conference on decision and control; Shaked, U., & Theodor, Y. (1992). \(H_∞\)Proceedings of IEEE conference on decision and control
[17] Shen, X.; Deng, L., Game theory approach to discrete \(H_∞\) filter design, IEEE Transactions on Signal Processing, 45, 1092-1095 (1997)
[18] Theodor, Y.; Shaked, U., Robust discrete-time minimum-variance filtering, IEEE Transactions on Signal Processing, 44, 181-189 (1996)
[19] Theodor, Y.; Shaked, U.; de Souza, C. E., A game theory approach to robust discrete time \(H_∞\)-estimation, IEEE Transactions on Signal Processing, 42, 1489-1491 (1994)
[20] Xie, L.; de Souza, C. E., \(H_∞\) filtering for linear periodic systems with parameter uncertainty, Systems & Control Letters, 17, 343-350 (1991) · Zbl 0748.93043
[21] Xie, L.; de Souza, C. E.; Wang, Y., Robust control of discrete time uncertain dynamical systems, Automatica, 29, 1133-1137 (1993) · Zbl 0776.93025
[22] Xie, L.; Soh, Y. C., Robust Kalman filtering with uncertain systems, Systems & Control Letters, 22, 123-129 (1994) · Zbl 0792.93118
[23] Xie, L.; Soh, Y. C., Guaranteed cost control of uncertain discrete-time systems, Control Theory and Advanced Technology, 10, 2, 1235-1251 (1995)
[24] Xie, L.; Soh, Y. C.; de Souza, C. E., Robust Kalman filtering with uncertain discrete-time systems, IEEE Transactions on Automatic Control, 39, 1310-1314 (1994) · Zbl 0812.93069
[25] Wang, Z.; Guo, Z.; Unbehauen, H., Robust \(H_2/H_∞\) state estimation for discrete-time systems with error variance constraints, IEEE Transactions on Automatic Control, 42, 1431-1435 (1997) · Zbl 0886.93059
[26] Wang, Z.; Unbehauen, H., Robust \(H_2/H_∞\) state estimation for systems with error variance constraintsthe continuous time case, IEEE Transactions on Automatic Control, 44, 1061-1065 (1999) · Zbl 0955.93052
[27] Wang, Z.; Zhu, J.; Unbehauen, H., Robust filter design with time-varying parameter uncertainty and error variance constraints, International Journal of Control, 72, 30-38 (1999) · Zbl 0953.93069
[28] Zhu, X., Soh, Y. C., & Xie, L. (2000). Feasibility and convergence analysis of discrete-time a priori filters. Proceedings of IEEE conference on decision and control; Zhu, X., Soh, Y. C., & Xie, L. (2000). Feasibility and convergence analysis of discrete-time a priori filters. Proceedings of IEEE conference on decision and control
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.