On robust Hurwitz polynomials

Abstract

In this note, Kharitonov's theorem on robust Hurwitz polynomials is simplified for low-order polynomials. Specifically, for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 3, 4</tex> , and 5, the number of polynomials required to check robust stability is one, two, and three, respectively, instead of four. Furthermore, it is shown that for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n \geq 6</tex> , the number of polynomials for robust stability checking is necessarily four, thus further simplification is not possible. The same simplifications arise in robust Schur polynomials by using the bilinear transformation. Applications of these simplifications to two-dimensional polynomials as well as to robustness for single parameters are indicated.