A generalization of Kharitonov´s four-polynomial concept for robust stability problems with linearly dependent coefficient perturbations

Kharitonov´s four-polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions. To this end, a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis. The present work is motivated by two fundamental limitations of Kharitonov´s theorem, namely: (1) the theorem only applies to polynomials with independent coefficient perturbations and (2) it only applies to zeros in the left-hand plane