H∞ state estimation via asynchronous filtering for descriptor Markov jump systems with packet losses

This paper is concerned with the problem of asynchronous state estimation for a class of discrete-time descriptor Markov jump systems with packet losses. Packet losses and asynchronous modes are simultaneously considered in the communication link between the plant and the estimator, where the missing probability of packet losses is governed by a binary distribution. Firstly, by constructing a stochastic Lyapunov functional, a sufficient condition is given such that the filtering error system is stochastically admissible and has a prescribed H∞ noise attenuation performance index. Then, based on the matrix inequality decoupling technique, a linear matrix inequality (LMI)-based condition on the existence of the H∞ asynchronous filter is presented, where the asynchronous filter can be of full-order or reduced-order. Compared with the previous methods, the proposed design method does not impose constraints on slack variables and dimensions of the designed filter, which shows less conservative results. Finally, numerical examples are given to illustrate the benefit and applicability of the new method.