Pole assignment with minimum eigenvalue differential sensitivity

Abstract

This paper introduces a set of mathematical formulae for calculating the eigenvalue differential sensitivities of the closed-loop state matrix with respect to the open-loop state matrix, input matrix and state feedback matrix. It provides a computational procedure for a robust pole assignment problem. The algorithm is based on a gradient flow minimization of a differentiate objective function which measures the sensitivity for all closed-loop poles. Two numerical examples are employed to illustrate the technique. Comparisons to other existing methods are made as well.