Robust \(H_\infty\) filtering for polytopic uncertain time-delay systems with Markov jumps. (English) Zbl 0998.93041

The paper is devoted to the analysis of a class of dynamical systems with abrupt changes in their structure. The system’s dynamics is given by a linear differential system with time delays; the parameters of the model are assumed to belong to a convex compact set of polytopic type. The goal of the work is to design a linear full order filter providing the necessary error of estimation. It is proved that under appropriate conditions the system is robust stochastically stable. The proofs are based on the construction of Lyapunov functions. A few numerical examples are worked out to illustrate the developed algorithms, including a system with Markov jumps.


93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
93E15 Stochastic stability in control theory
93C23 Control/observation systems governed by functional-differential equations
93C05 Linear systems in control theory
60J75 Jump processes (MSC2010)
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