A new Lyapunov technique for robust control of systems with uncertain non-small delays

Stability, L2-gain analysis and state-feedback H∞ control of linear systems with uncertain time-varying delays are considered in the case, where the nominal values of delays are constant and non-zero. A new construction of Lyapunov–Krasovskii functionals (LKFs) is introduced: to a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturbed system and that vanish when the delay perturbations approach 0. In the present paper we apply the nominal Lyapunov–Krasovskii functional (LKF) which is based on the descriptor model transformation. Sufficient conditions are given in terms of linear matrix inequalities. Numerical examples illustrate the efficiency of the method.