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.
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