A Stochastic Sampled-Data Approach to Distributed $H_{\infty }$ Filtering in Sensor Networks

In this paper, the problem of distributed H∞ filtering in sensor networks using a stochastic sampled-data approach is investigated. A set of general nonlinear equations described by sector-bounded nonlinearities is utilized to model the system and sensors in networks. Each sensor receives the information from both the system and its neighbors. The signal received by each sensor is sampled by a sampler separately with stochastic sampling periods before it is employed by the corresponding filter. By converting the sampling periods into bounded time-delays, the design problem of the stochastic sampled-data based distributed H∞ filters amounts to solving the H∞ filtering problem for a class of stochastic nonlinear systems with multiple bounded time-delays. Then, by constructing a new Lyapunov functional and employing both the Gronwall's inequality and the Jenson integral inequality, a sufficient condition is derived to guarantee the H∞ performance as well as the exponential mean-square stability of the resulting filtering error dynamics. Subsequently, the desired sampled-data based distributed H∞ filters are designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed sampled-data distributed H∞ filtering scheme.