Persistent bounded disturbance rejection for discrete time-delay systems using output feedback

In this paper, we provide a novel solution to the problem of persistent bounded disturbance rejection in linear discrete-time systems with time-varying delays. The solution is developed based on the tools of invariant set analysis and Lyapunov-Krasovskii functional method. As an integral part of the solution, we derive less conservative sufficient conditions on robust attractor for discrete-time systems with delays in terms of strict linear matrix inequalities (LMIs) to guarantee that the desired ℓ1-performance is achieved. A robust dynamic output-feedback controller with arbitrary order is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example.