EXTREME POINT RESULTS FOR ROBUST STABILITY OF INTERVAL PLANTS: BEYOND FIRST ORDER COMPENSATORS

Abstract

Motivated by robust stabilization of interval plants, this paper concentrates on a fundamental problem involving a family of polynomials obtained via convex combination of “extreme members.” The objective is to provide conditions under which stability of the extremes implies stability of the entire family. Although the existing literature contains rather strong extreme point results involving frequency domain analysis, there is a paucity of more direct coefficient space criteria—this paper deals exclusively with the coefficient space problem. To this end, we introduce the so-called Alternating Hurwitz Minor Condition (AHMC) and show how it can be used to enlarge the class of polynomial families for which extreme point results can be obtained. Subsequently, the ramifications on robust stability of interval plants are fully explained. In contrast to existing literature for first order compensators, the AHMC makes it possible to deal with classes of higher order compensators in an extreme point context.