$H_\infty$ Filtering for Networked Systems With Multiple Time-Varying Transmissions and Random Packet Dropouts

This paper is concerned with the H_∞ filtering for networked systems with multiple time-varying transmissions and random packet dropouts. We design a remote H_∞ filter for these two networked issues such that the filtering error system is exponentially stable and achieves a prescribed H_∞ performance level. A switched system approach is used to model the multiple time-varying transmission process, and a set of stochastic variables are employed to describe the random packet dropout phenomenon. By the switched system theory and some stochastic analysis methods, a sufficient condition for the existence of the H_∞ filter is derived in terms of linear matrix inequalities (LMIs). Moreover, the filter gains are determined by solving an optimization problem. Two numerical examples are given to illustrate the effectiveness of the proposed design method.