Robust stability, stabilization, and H ∞ control of a class of nonlinear discrete time stochastic systems

Abstract

This paper studies robust stability, stabilization, and H ∞ control for a class of nonlinear discrete time stochastic systems. Firstly, the easily testing criteria for stochastic stability and stochastic stabilizability are obtained via linear matrix inequalities (LMIs). Then a robust H ∞ state feedback controller is designed such that the concerned system not only is internally stochastically stabilizable but also satisfies robust H ∞ performance. Moreover, the previous results of the nonlinearly perturbed discrete stochastic system are generalized to the system with state, control, and external disturbance dependent noise simultaneously. Two numerical examples are given to illustrate the effectiveness of the proposed results.