Zhu, Xing; Soh, Yeng Chai; Xie, Lihua Design and analysis of discrete-time robust Kalman filters. (English) Zbl 1001.93078 Automatica 38, No. 6, 1069-1077 (2002). The authors consider the problem of robust a priori Kalman filtering (an estimator is called an a priori filter if it is obtained from the output measurements) for discrete-time systems with norm-bounded parameter uncertainty in both the state and output matrices. The uncertain discrete-time system has the form \[ x_{k+1}=(A+{\Delta}A_{k+1})x_{k}+B{\omega}_{k},\;y_{k}=(C+{\Delta}C_{k})x_{k}+v_{k}, \] where \({\Delta}A_{k}\) and \({\Delta}C_{k}\) are unknown matrices which represent time-varying parameter uncertainties. The problem consists in the design of linear filters that yield an estimation error variance with a guaranteed upper bound for all admissible uncertainties. Both the finite-horizon and infinite-horizon cases are investigated, and, under the notion of robust quadratic filters, necessary and sufficient conditions for the design of such a filter with an optimized upper bound of error covariance are given in terms of a pair of Riccati difference equations. Feasibility and convergence properties of the robust quadratic filters are also analyzed. Reviewer: Yu.S.Mishura (Kyïv) Cited in 30 Documents MSC: 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems Keywords:uncertain discrete-time systems; robust state estimation; Kalman filtering; bounded variance; quadratic filters; Riccati difference equations PDFBibTeX XMLCite \textit{X. Zhu} et al., Automatica 38, No. 6, 1069--1077 (2002; Zbl 1001.93078) Full Text: DOI References: [1] Anderson, B. D.O; Moore, J. B., Optimal filtering (1979), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0688.93058 [2] Bolzern, P.; Colaneri, P.; de Nicolao, G., Finite escapes and convergence properties of guaranteed-cost robust filters, Automatica, 33, 31-47 (1997) · Zbl 0870.93040 [3] Fu, M., de Souza, C. E., & Luo, Z. Q. (1999). Finite horizon robust Kalman filter design, Proceedings of the 38th IEEE conference on decision and control; Fu, M., de Souza, C. E., & Luo, Z. Q. (1999). Finite horizon robust Kalman filter design, Proceedings of the 38th IEEE conference on decision and control [4] Petersen, I. R.; McFarlane, D. C., Optimal guaranteed cost filtering for uncertain discrete-time linear systems, International Journal of Robust and Nonlinear Control, 6, 267-280 (1996) · Zbl 1035.93509 [5] Shaked, U.; de Souza, C. E., Robust minimum variance filtering, IEEE Transactions on Signal Processing, 43, 2474-2483 (1995) [6] Theodor, Y.; Shaked, U., Robust discrete-time minimum-variance filtering, IEEE Transactions on Signal Processing, 44, 181-189 (1996) [7] Wang, Z.; Zhu, J.; Unbehauen, H., Robust filter design with time-varying parameter uncertainty and error variance constraints, International Journal of Control, 72, 1, 30-38 (1999) · Zbl 0953.93069 [8] Xie, L.; Soh, Y. C., Guaranteed cost control of uncertain discrete-time systems, Control Theory and Advanced Technology, 10, 4, 1235-1251 (1995) [9] Xie, L.; Soh, Y. C.; de Souza, C. E., Robust Kalman filtering for uncertain discrete-time systems, IEEE Transactions on Automatic Control, 39, 1310-1314 (1994) · Zbl 0812.93069 [10] Zhu, X., Soh, Y. C., & Xie, L. (2000). Feasibility and convergence analysis of discrete-time \(H_∞\)Proceedings of the 2000 American Control Conference; Zhu, X., Soh, Y. C., & Xie, L. (2000). Feasibility and convergence analysis of discrete-time \(H_∞\)Proceedings of the 2000 American Control Conference 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.