Homogeneous polynomial Lyapunov functions for the analysis of polytopic parameter-dependent descriptor systems

Abstract

In this paper, we present an extension of the homogeneous polynomial Lyapunov functions (HPLFs) approach previously developed for uncertain standard systems to the case of uncertain continuous-time descriptor ones. By employing a new power transformation of the state vector with respect to its dynamic and algebraic parts, new necessary and sufficient admissibility analysis conditions are developed based on such a class of Lyapunov functions. The presented results deal with time-varying parameters with both unbounded variation rates, based on parameter-independent HPLFs, and bounded variation rates lying inside a polytope by exploiting polytopic parameter-dependent HPLFs. Numerically, well tractable sufficient LMI conditions are also derived for both cases. A comparison with results from the literature is performed, showing the reduction of conservatism throughout the novel conditions presented in this article.