Análise de estabilidade robusta de sistemas lineares incertos utilizando o critério de Liénard-Chipart

Abstract

This paper presents a numerical comparison among methods that certify the robust stability of a continuous-time linear system with an uncertain parameter belonging to an interval by means of the positivity analysis of polynomials associated with the Liénard-Chipart stability criterion. To certify the positivity of the polynomials, a technique of coefficient verification through Polya's Theorem is proposed and compared with sum-of-squares decomposition and global optimization based on theory of moments. A strategy of division of the uncertain domain is also implemented to allow the methods to be conclusive. Numerical comparisons show the better performance of the verification based on Polya's Theorem with respect to the optimization-based procedures.