Stability and guaranteed cost control of uncertain discrete delay systems

Robust stability and the guaranteed cost control problem are considered for discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov-Krasovskii functionals (LKFs), which has been recently introduced in the continuous-time case, is applied. To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the system with the perturbed delays and that vanish when the delay perturbations approach zero. The nominal LKF is chosen in the form of the descriptor type and is applied either to the original or to the augmented system. The delay-independent result is derived via the Razumikhin approach. Guaranteed cost state-feedback control is designed. The advantage of the new tests is demonstrated via illustrative examples.