A Generalization of Kharitonov's Four Polynomial Concept for Robust Stability Problems with Linearly Dependent Coefficient Perturbations

Abstract

From a systems-theoretic point of view, Kharitonov's seminal theorem on stability of interval polynomials suffers from two fundamental limitations: First, the theorem only applies to polynomials with independent coefficient perturbations. Note that uncertainty in the physical parameters of a linear system typically results in dependent perturbations in the coefficients of the characteristic polynomial. Secondly, Kharitonov's Theorem only applies to zeros in the left half plane?more general zero location regions are not accommodated. In view of this motivation, the main result of this paper is a generalization of Kharitonov's four polynomial concept to the case of linearly dependent coefficient perturbations and more general zero location regions.