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Robust mode-independent filtering for discrete-time Markov jump linear systems with multiplicative noises. (English) Zbl 1278.93263

Summary: This paper deals with the robust mode-independent linear filtering problem for discrete-time Markov jump linear systems with multiplicative noises. It is assumed that the values of the Markov chain are not available and that the parameters of the systems are subject to convex polytopic uncertainties. The goal is to design a mode-independent (that is, one that doesn’t depend on the Markov jump parameter) dynamic linear filter such that the closed loop system is mean square stable and minimises an upper bound for the stationary expected value of the square error. A Linear Matrix Inequalities (LMI) formulation, based on a parameter dependent Lyapunov procedure, is proposed to solve the problem. The paper concludes with an illustrative example.

MSC:

93E11 Filtering in stochastic control theory
93C55 Discrete-time control/observation systems
60J75 Jump processes (MSC2010)
93C05 Linear systems in control theory
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