Robust Finite-Time $H_{{\infty}}$ Filtering for Uncertain Discrete-Time Nonhomogeneous Markovian Jump Systems

This paper investigates the problem of finite-time $H_{\infty }$ filtering for uncertain discrete-time Markovian jump systems. The parameter uncertainties in the dynamic systems are modeled to satisfy the norm-bounded condition. The transition probabilities are assumed to be time-varying and described as convex polyhedron. Based on the stochastic finite-time bounded analysis and linear matrix inequality technique, an $H_{\infty }$ filter is designed and sufficient criteria are established, which guarantee the filtering error system to be finite-time bounded in $H_{\infty }$ sense. Two examples are presented to demonstrate the usefulness and applicability of the proposed method.