Robust Mixed H2/h∞ Control for Systems with Stochastic Nonlinearity

In this paper, the problem of mixed H2/H∞ 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 H2/H∞ control problem is formulated in terms of the notion of exponentially mean-square quadratic stability, and the characterizations of both the H2 control performance and the H∞ 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 H2/H∞ control problem by using a linear matrix inequality (LMI) approach.Copyright c © 2005 IFAC