Discontinuous Lyapunov approach to state estimation and filtering of jumped systems with sampled-data

This paper is concerned with the sampled-data state estimation and H∞H∞ filtering for a class of Markovian jump systems with the discontinuous Lyapunov approach. The system measurements are sampled and then transmitted to the estimator and filter in order to estimate the state of the jumped system under consideration. The corresponding error dynamics is represented by a system with two types of delays: one is from the system itself, and the other from the sampling period. As the delay due to sampling is discontinuous, a corresponding discontinuous Lyapunov functional is constructed, and sufficient conditions are established so as to guarantee both the asymptotic mean-square stability and the H∞H∞ performance for the filtering error systems. The explicit expressions of the desired estimator and filter are further provided. Finally, two simulation examples are given to illustrate the design procedures and performances of the proposed method.