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.