This paper deals with the problems of robust stabilization and H∞ control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm-bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed-loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H∞ control problem is to guarantee a specified H∞ performance index, while still achieving the mean-square exponential stability requirement for the closed-loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H∞ control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI-based design methods.
