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This paper is concerned with the problems of robust stochastic stabilization and robust H∞ control for uncertain discrete-time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time-varying norm-bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed-loop system irrespective of all admissible parameter uncertainties; while for the robust H∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.
Xu et al. (Sat,) studied this question.