Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers

Abstract

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.