STRUCTURAL STABILIZATION OF UNCERTAIN SYSTEMS: NECESSITY OF THE MATCHING CONDITION.

Abstract

This paper investigates one aspect of the problem of stabilizing an uncertain linear system. That is, the systems under consideration contain uncertain parameters which are unknown but bounded. The question arises as to whether such a system can be stabilized via feedback control. In some of the previous papers in this area, the system is assumed to satisfy a so-called 'matching-condition; ' this type of assumption is used to assure that the uncertain system can be stabilized. It is known, however, that the matching condition is not a necessary condition for stabilizability. This paper introduces a strengthened notion of stabilizability referred to as structural stabilizability via a nominally determined quadratic Lyapunov function. It is then shown that if a system is to have this stronger property, the matching condition must necessarily be satisfied.