Optimal Guaranteed Cost Control of Uncertain Discrete Systems with Both State and Input Delays: New LMI-Based Characterization and Methods

This paper addresses the guaranteed cost control for a class of uncertain discrete-time systems with both state and input delays. New linear matrix inequalities (LMI) characterizations are proposed for the existence of a state feedback controller which guarantees not only the asymptotic stability of the closed-loop system, but also an adequate performance bound over all the possible parameter uncertainties. A procedure is given to select a suitable state feedback controller that minimizes a bound on a quadratic performance index. The result exhibits some favorable features in computation which is shown by a numerical example