Probability-Guaranteed Distributed Filtering for Nonlinear Systems on Basis of Nonuniform Samplings Subject to Envelope Constraints

This paper investigates the probability-guaranteed distributed $H_\infty$ filtering problem for stochastic time-varying systems over sensor networks. The measurements from sensing nodes are sampled nonuniformly before being received by filters and the sampling processes are modeled by a set of Markov chains. The purpose of the addressed problem is to design a distributed filter algorithm which meets the finite-horizon average $H_\infty$ performance, meanwhile guaranteeing all filtering errors bounded within a prespecified envelope with a certain probability. Sufficient conditions for the feasibility of the mentioned filtering technique are established using convex optimization techniques. The desired filtering gains are subsequently determined by resolving the relevant matrix inequalities at each time step. Finally, the effectiveness of the proposed filtering algorithm is shown via an illustrative numerical example.