Robust Stability Analysis in the Presence of Time-Varying Uncertainties and Time Delay

The paper presents some robust stability conditions for systems affected by parametric uncertainties and time delay. The objective is to obtain a method allowing determining the admissible domain of the parametric uncertainties and the maximum value of the time delay that can be reached without destabilizing the system. The bounds of the parametric uncertain are obtained using the Small Gain Theorem. The norm-boundedness is studied using a version of the Bounded Real Lemma for time-delayed systems. Throughout the paper the theoretical developments are illustrated using a numerical example concerning the prediction of pilot induced oscillations (PIO).