Stability Feeler: A Tool for Analysis of Polytopic Polynomials

Abstract

Stability analysis of a linear uncertain polynomial system in real parameter space is one of central themes of recent control theory. It is generally very difficult to analyze the stability of such a system because the number of its characteristic polynomials to be analyzed becomes enormous. A parallelotope of polynomials is a typical type of uncertain polynomials. Though a number of analysis methods for such a parallelotope are at our hand, they mainly focus on stability check of given polynomials and hardly give information on how for the certain interested parameter can be extended for stability. To solve this problem, we propose a novel tool for stability analysis called “Stability Feeler". This concept leads to an algorithm which determines D-stability intervals along a given line in the polynomial coefficient space. With the tool, stability problems of parallelotopes can be successfully resolved. Two numerical examples are shown to support this concept.