H∞ Filter Design for Networked Control Systems: A Markovian Jump System Approach

Abstract

This paper puts forward a method to design the H∞ filter for networked control systems (NCSs) with time delay and data packet loss. Based on the properties of Markovian jump system, the packet loss is treated as a constant probability independent and identically distributed Bernoulli random process. Thus, the stochastic stability condition can be acquired for the filtering error system, which meets an H∞ performance index level γ. It is shown that, by introducing a special structure of the relaxation matrix, a linear representation of the filter meeting an H∞ performance index level for NCSs with time delay and packet loss can be obtained, which uses linear matrix inequalities (LMIs). Finally, numerical simulation examples demonstrate the effectiveness of the proposed method.