A SURVEY OF EXTREME POINT RESULTS FOR ROBUSTNESS OF CONTROL-SYSTEMS

This paper surveys a subset of the body of research which was sparked by Kharitonov's Theorem. The focal point is extreme point results for robust stability and robust performance. That is, we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family. The results which are surveyed apply mainly to systems with structured real parametric uncertainty. In addition, a number of counterexamples are given to illustrate cases for which an extreme point result does not hold. For such cases, a solution via the so-called Edge Theorem is often possible.