Optimal robust filtering for uncertain discrete-time systems (Q2725120)
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scientific article; zbMATH DE number 1618786
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal robust filtering for uncertain discrete-time systems |
scientific article; zbMATH DE number 1618786 |
Statements
4 March 2004
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robust filtering
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linear discrete-time systems
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norm-bounded parameter uncertainty
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Riccati equations
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upper bound
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variance of the estimation error
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Optimal robust filtering for uncertain discrete-time systems (English)
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The robust filtering problem for linear discrete-time systems with norm-bounded parameter uncertainty in the state- and output-matrices [cf. \textit{L. Xie}, \textit{Y. C. Soh} and \textit{C. E. de Souza}, IEEE Trans. Autom. Control 39, 1310-1314 (1994; Zbl 0812.93069)] is studied. Via introducing the related Riccati equations, an upper bound for the variance of the estimation error of the linear filter is obtained. Necessary and sufficient conditions for the existence of an optimal robust filter are then equivalently guaranteed via the existence and the stability of the solutions of two algebraic Riccati equations proposed here. The state-space formulas for the optimal robust filter proposed here are optimal with respect to the error variance upper bound, and thus the robust Kalman filter proposed in the above-mentioned paper was suboptimal in this sense.
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