Robust mixed H2/H1 control for a class of nonlinear stochastic systems

The problem of mixed H2/H1 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/H1 control problem is formulated in terms of the notion of exponentially mean-square quadratic stability and the characterisations of both the H2 control performance and the H1 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 uncertainities. A unified framework is established to solve the addressed mixed H2/ H1 control problem using a linear matrix inequality approach. Within such a framework, two additional optimisation problems are discussed, one is to optimise the H1 robustness performance, and the other is to optimise the H2 control performance. An illustrative example is provided to demonstrate the effectiveness of the proposed method.