Robust Mixed H_2/H_infinity Control for Systems with Stochastic Nonlinearity

In this paper, the problem of mixed H_2/H_infinity control is considered for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities are described by statistical means of the stochastic variables, and the uncertainties are represented by deterministic norm-bounded parameter perturbations. The mixed H_2/H_infinity control problem is formulated in terms of the notion of exponentially mean-square quadratic stability, and the characterizations of both the H_2 control performance and the H_infinity robustness performance. A new technique is developed to deal with the matrix trace terms arising from the stochastic nonlinearities, and the well-known S-procedure is adopted to handle the deterministic uncertainties. A unified framework is established to solve the addressed mixed H_2/H_infinity control problem by using LMI approach.