A New Algorithm for Testing the Stability of a Polytope: A Geometric Approach for Simplification

Abstract

Considered in this paper is the robust stability of a class of systems in which a relevant characteristic equation is a family of polynomials F: f(s, q) = a0 (q) + a1 (q )s + [[ellipsis]] + a n (q)sn with its coefficients ai (q) depending linearly on q unknown-but-bounded parameters, q = (p1 , p2 , [[ellipsis]], pq )T . It is known that a necessary and sufficient condition for determining the stability of such a family of polynomials is that polynomials at all the exposed edges of the polytope of F in the coefficient space be stable (the edge theorem of Bartlett et al., 1988). The geometric structure of such a family of polynomials is investigated and an approach is given, by which the number of edges of the polytope that need to be checked for stability can be reduced considerably. An example is included to illustrate the benefit of this geometric interpretation.