Finite-Time H∞ Filtering for Nonlinear Singular Systems With Nonhomogeneous Markov Jumps

This paper addresses the finite-time H-infinity filtering for a class of nonlinear singular nonhomogeneous Markov jump systems by T-S fuzzy approximation approach, where the transition probabilities (TPs) are time-varying and unknown. First, by considering a stochastic Lyapunov functional and rendering the time-varying TPs inside a polytope, a sufficient condition on singular stochastic H-infinity finite-time boundedness (SSH infinity FTB) for the filtering error systems is given. Then, by using the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition on the existence of the finite-time H-infinity fuzzy filter is presented. The fuzzy filter is developed in terms of LMIs ensuring the filtering error system is SSH infinity FTB. Compared with the previous ones, the proposed design method in this paper has more freedom, leading to less conservative results. A tunnel diode circuit is provided to illustrate the effectiveness and advantage of the design approach proposed in this paper.