ON ROBUST STABILITY VIA COMPLETE LYAPUNOV KRASOVSKII FUNCTIONAL

Stability of linear systems with norm-bounded uncertainties and uncertain time-varying delays is considered. The delays are supposed to be bounded and fast-varying (without any constraints on the delay derivative). Sufficient stability conditions are derived via complete Lyapunov-Krasovskii functional (LKF). A new LKF construction, which was recently introduced for systems with uncertain delays, is extended to the case of norm-bounded uncertainties: to a nominal LKF, which is appropriate to the system with the nominal value of the coefficients and of the delays, terms are added that correspond to the perturbed system and that vanish when the uncertainties approach 0. Numerical examples illustrate the efficiency of the method.