Robust \(H_\infty\) filtering for a class of uncertain Markovian jump systems with time delays (Q474375)

Summary: This paper studies the problem of robust \(H_\infty\) filtering for a class of uncertain time-delay systems with Markovian jumping parameters. The system under consideration is subject to norm-bounded time-varying parameter uncertainties. The problem to be addressed is the design of a Markovian jump filter such that the filter error dynamics are stochastically stable and a prescribed bound on the \(H_\infty\)-induced gain from the noise signals to the filter error is guaranteed for all admissible uncertainties. A sufficient condition for the existence of the desired robust \(H_\infty\) filter is given in terms of two sets of coupled algebraic Riccati inequalities. When these algebraic Riccati inequalities are feasible, the expression of a desired \(H_\infty\) filter is also presented. Finally, an illustrative numerical example is provided.