Abstract

We consider the robust stability problem for a class of uncertain neutral time-delay systems where the characteristic equations involve a polytope p of quasipolynomials of neutral type. Given a stability region D in the complex plane our goal is to find a constructive technique to verify the D-stability of p (i.e. to verify whether the roots of every quasipolynomial in p all belong to D). We first show that, under a certain assumption on the stability region D, p is D-stable if and only if the edges of p are D-stable. Hence, the D-stability problem of a higher dimensional polytope is reduced to the D-stability problem of a finite number of pairwise convex combinations of vertices. Based on this result, we then give an effective graphical test for checking the D-stability of a polytope of quasipolynomials of neutral type.

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