Structured phase margin for stability analysis of linear systems with time-delay

Abstract

In this paper, we introduce the notion of structured phase margin for characterizing stability margins in terms of a nominal plant transfer function in the presence of unknown structured phase perturbations. Furthermore, since the structured phase margin may be difficult to compute in general, we derive a lower bound in terms of a generalized eigenvalue problem. This bound is constructed by choosing stability multipliers that are tailored to the structure of the phase uncertainty. Finally, using the structured phase margin framework developed in the paper, we present new and improved frequency-domain, delay-dependent stability criteria for stability analysis of time-delay systems.