Robust H2 filtering for a class of systems with stochastic nonlinearities

This paper addresses the robust H₂ filtering problem for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities described by statistical means in this paper comprise some well-studied classes of nonlinearities in the literature. A technique is developed to tackle the matrix trace terms resulting from the nonlinearities, and the well-known S-procedure technique is adopted to cope with the uncertainties. A unified framework is established to solve the addressed robust H₂ filtering problem by using a linear matrix inequality approach. A numerical example is provided to illustrate the usefulness of the proposed method.