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Reduced-order \(H_{\infty}\) filtering for linear systems with Markovian jump parameters. (English) Zbl 1129.93542
Summary: This paper addresses the reduced-order \(H_{\infty}\) filtering problem for continuous-time Makovian jump linear systems, where the jump parameters are modelled by a discrete-time Markov process. Sufficient conditions for the existence of the reduced-order \(H_{\infty}\) filter are proposed in terms of linear matrix inequalities (LMIs) and a coupling non-convex matrix rank constraint. In particular, the sufficient conditions for the existence of the zero-order \(H_{\infty}\) filter can be expressed in terms of a set of strict LMIs. The explicit parameterization of the desired filter is also given. Finally, a numerical example is given to illustrate the proposed approach.

MSC:
93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
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