$H_{\infty}$ Filtering for Networked Control Systems with Two-Channel Packet Dropouts and Mixed Random Delays Using Delta Operator

In this paper, the problem of H∞ filtering for networked control systems using delta operator is investigated, which includes two-channel packet dropouts and mixed random delays. Random communication packet dropouts exist in both channels from sensors to controllers and from controllers to actuators. They are represented by two independent Bernoulli distributed white sequences. The mixed random time-delays consist of network induced time delay and discrete infinite distributed delays. A networked-based model is considered with a Markov stochastic process and the H_∞ filtering error system is constructed by using Lyapunov-Krasovskii functional in delta domain. A sufficient condition for stochastic stability of the filtering error system with an H_∞ performance is obtained in terms of linear matrix inequalities (LMI). The explicit expression of the desired H_∞ filter is given. A numerical example shows the effectiveness of the proposed method.