Robustness of pole location in perturbed systems

In this paper we present some results on robustness of location of roots of polynomials in given regions of the complex plane for unknown but bounded perturbations on the polynomial coefficients. A geometric approach in coefficient space is exploited to derive maximal deviations (in a given class of admissible perturbations) of characteristic polynomial coefficients of an uncertain linear system from their nominal values preserving system poles in a given region of the complex plane. It is also shown that the solution of this problem can be used to give computationally feasible necessary and sufficient conditions such that all the roots of the members of a family of polynomials lie in a given open region of the complex plane. This last result can be considered an extension of the result of the well-known theorem of Kharitonov. It is also outlined how the proposed technique can be used to deal with families of polynomials with linearly correlated coefficient perturbations