A Markovian system approach to distributed H∞ filtering for sensor networks with stochastic sampling

This paper is concerned with the distributed H∞ filtering problem for a class of sensor networks with stochastic sampling. System measurements are collected through a sensor network stochastically and the phenomena such as random measurement missing and quantization are also considered. Firstly, the stochastic sampling process of the sensor network is modeled as a discrete-time Markovian system. Then, the logarithmic quantization effect is transformed into the parameter uncertainty of the filtering system, and a set of binary variables is introduced to model the random measurement missing phenomenon. Finally, the resulting augmented system is modeled as an uncertain Markovian system with multiple random variables. Based on the Lyapunov stability theory and the stochastic system analysis method, a sufficient condition is obtained such that the augmented system is stochastically stable and achieves an average H∞ performance level γ; the design procedure of the optimal distributed filter is also provided. A numerical example is given to demonstrate the effectiveness of the proposed results.