A Phase Diagram Approach to Robust Stability Analysis

Abstract

Using a novel phase diagram, this paper investigates the robust stability of polytopes of quasipolynomials. These sets of quasipolynomials are useful in modeling delay systems that are subject to parameter uncertainties. For many stability investigations, it has previously been shown that polytopes of quasipolynomials can be analyzed using only their edges. It has also been shown how to test the stability of each edge using a phase condition. This paper shows how to use this phase condition in an easily constructed diagram that tests the stability of all edges simultaneously rather than one at a time. Use of this diagram reducesthe effort needed to test stability and provides some interesting information.