On design of robust ℋ∞ filters for uncertain Markovian stochastic systems

The problem of designing robust ℋ_∞ filters for uncertain Markovian stochastic systems with time-varying delays is addressed in this paper. It is assumed that the Markovian systems are perturbed by Itô-type stochastic disturbances and subjected to parametric uncertainties and mode transition rate uncertainties. The main specification of robust ℋ_∞ filters under design is to ensure that the filtering error system is robustly stochastically stable and a prescribed ℋ_∞ disturbance attenuation level is met in the face of all admissible parameter uncertainties and time-delays. It is shown that the desired robust ℋ_∞ filters can be readily designed by solving some linear matrix inequalities which are derived by using a stochastic Lyapunov-Krasovskii functional and the free-weighting matrix technique.