Distributed Sampled-Data ${H_\infty }$ Filtering for Sensor Networks With Nonuniform Sampling Periods

This paper presents a switched system approach to solving the distributed sampled-data
$\mbi{H_\infty }$
filtering problem for sensor networks with nonuniform sampling periods. The sensor network is considered to be a peer-to-peer network without an estimation center. The measurements are sampled with nonuniform sampling periods, and each sensor in the network collects the sampled measurements only from its neighbors and runs a distributed
$\mbi{H_\infty }$
filtering algorithm to generate estimates. A stochastic switched system model is proposed to describe the aperiodic sampled-data filtering system with random packet losses. A sufficient existence condition for the distributed
$\mbi{H_\infty }$
filters is derived by using the average dwell time method, and it is shown that the obtained condition critically depends on the sampling periods and the packet loss probabilities. The design of the filters is accomplished by solving a convex optimization problem, and the designed filters guarantee that the filtering system is mean-square exponentially stable and all the filtering errors satisfy an average
$\mbi{H_\infty }$
noise attenuation level. An illustrative example is finally given to show the effectiveness of the proposed results.