L2 − L∞ filtering for Markovian jump systems with time-varying delays and partly unknown transition probabilities

This paper considers the L2 − L∞ filtering problem for Markovian jump systems. The systems under consideration involve time-varying delays, disturbance signal and partly unknown transition probabilities. The aim of this paper is to design a filter, which is suitable for exactly known and partly unknown transition probabilities, such that the filtering error system is stochastically stable and a prescribed L2 − L∞ disturbance attenuation level is guaranteed. By using the Lyapunov–Krasovskii functional, sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of filter design for Markovian jump systems with partly unknown transition probabilities.

► The condition on stochastic stability of MJSs with partly unknown transition probabilities is present.
► The results do not require the complete knowledge of the transition probabilities.
► The designed filters are feasible and effective despite the partly unknown transition probabilities.