Distributed $H_{\infty }$ Filtering for Polynomial Nonlinear Stochastic Systems in Sensor Networks

In this paper, the distributed H_∞ filtering problem is addressed for a class of polynomial nonlinear stochastic systems in sensor networks. For a Lyapunov function candidate whose entries are polynomials, we calculate its first- and second-order derivatives in order to facilitate the use of Itô´s differential rule. Then, a sufficient condition for the existence of a feasible solution to the addressed distributed H_∞ filtering problem is derived in terms of parameter-dependent linear matrix inequalities (PDLMIs). For computational convenience, these PDLMIs are further converted into a set of sums of squares that can be solved effectively by using the semidefinite programming technique. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.