Robust Filtering for a Class of Uncertain Markovian Jump Systems with Time Delays

This paper studies the problem of robust 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 -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 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 filter is also presented. Finally, an illustrative numerical example is provided.