Robust stability and performance in the presence of real parameter perturbation-a unified analysis approach

This study deals with the stability and performance conditions of a closed loop system whose A matrix depends linearly on the magnitude bounded real parameter perturbation. An analysis approach based on the existence of a common solution P=P´⩾0 to the infinite set of Riccati equations corresponding to the perturbed region in the parameter space is discussed. Two methods of transforming that infinite-dimensional problem into a finite-dimensional one are shown. An alternative proof that the method based on the single Riccati equation can be equally conservative as the one based on the small gain theorem is presented