H∞ filtering for a class of networked systems with stochastic sampling—A Markovian system approach

This paper is concerned with the H_∞ filtering for a class of networked systems with stochastic sampling, signal quantization and random packet dropouts. The measurement signal is sampled stochastically, then quantized and transmitted to the filter via a communication network. We first model the stochastic sampling process as a Markovian system, and handle the logarithmic quantization by the sector bound approach, then a binary variable is introduced to model the networked communication process, the considered filtering system is finally modeled as a Markovian system with stochastic variables and an uncertainty. Based on the Lyapunov stability theory and the stochastic analysis method, a sufficient condition is obtained such that the filtering error system is stochastically stable and with a prescribed H_∞ performance level. The optimal filter design method is also provided. A numerical example is given to show the effectiveness of the proposed design.