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Design and analysis of discrete-time robust Kalman filters. (English) Zbl 1001.93078

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.

MSC:

93E11 Filtering in stochastic control theory
93C55 Discrete-time control/observation systems
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