Robust passive control for uncertain discrete-time systems with time-varying delays

This paper considers the problem of robust passive 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 state feedback controller and a dynamic output feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented, which is dependent on the size of the delay. When the linear matrix inequality is feasible, the explicit expression of the desired state feedback controller and output feedback controller are given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.