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

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 characterisations 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 uncertainities. A unified framework is established to solve the addressed mixed H₂/H_∞ control problem using a linear matrix inequality approach. Within such a framework, two additional optimisation problems are discussed, one is to optimise the H_∞ 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.