Robust control with maximal decay rate for linear discrete-time stochastic systems

The problems of robust stabilization and robust H ∞ control with maximal decay rate are investigated for discrete-time stochastic systems with time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, an optimal state feedback controller is designed, which ensures that the closed-loop system is robustly stochastically stable with maximal decay rate, while for the robust H ∞ control problem, the designed state feedback controller guarantees that the resulting closed-loop system is with a specified H ∞ performance level, besides robust stochastic stability with maximal decay rate. The method based on the convex optimization and linear matrix inequality is developed to solve these problems. Two examples are provided to show the effectiveness of the proposed approach.