A Class of Kharitonov Regions for Robust Stability of Linear Uncertain Systems

In this paper the Kharitonov´s Theorems [1,2] are generalized to the problem of so-called Kharitonov regions for robust stability of linear uncertain systems. Given a polytope of (characteristic) polynomials P and a stability region D in the complex plane, P is called D-stable if the zeros of every polynomial in P are interior to D. It is of interest to know whether D is a Kharitonov region, that is, whether the D-stability of the vertices of P implies the D-stability of P. A simple approach is developed which unifies and generalizes many known results on this problem.