Estimating the conservatism of Popov's criterion for real parametric uncertainties

We consider the problems of robust stability and performance analysis of linear systems subject to parametric uncertainties. The Popov criterion provides lower bounds of stability margins and upper bounds on robust performance. In this paper we propose a method for obtaining upper bounds on stability margin or lower bounds on robust H2 performance based on the outcome of the lower bound computation for the stability problem or the upper bound computation for the H2 performance problem. We make several numerical tests. © 1997 Elsevier Science B.V.