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

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.