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This paper deals with the problems of robust stabilization and robust H∞ control for discrete stochastic systems with time-varying delays and time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed-loop system for all admissible uncertainties, while for the robust H∞ control problem, a state feedback controller is designed such that, in addition to the requirement of the robust stochastic stability, a prescribed H∞ performance level is also required to be satisfied. A linear matrix inequality (LMI) approach is developed to solve these problems, and delay-dependent conditions for the solvability are obtained. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. An example is provided to demonstrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]

This paper considers the problem of robust H∞ control for uncertain discrete systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and measured output matrices. Attention is focused on the design of a full-order exponential stable dynamic output feedback controller which guarantees the exponential stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of this problem is presented, which is dependent on the size of the delay. When this LMI is feasible, the explicit expression of the desired output feedback controller is also given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]

This paper investigates the problem of H∞ model reduction for linear discrete-time singular systems. Without decomposing the original system matrices, necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. When these conditions are feasible, an explicit parametrization of the desired reduced-order models is given. Particularly, a simple LMI condition without rank constraint is derived for the zeroth-order H∞ approximation problem. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach. [Copyright &y& Elsevier]