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.

在本文中，我们将之前为不确定标准系统开发的齐次多项式 Lyapunov 函数 (HPLF) 方法扩展到不确定连续时间描述符系统的情况。通过对状态向量的动态部分和代数部分进行新的幂变换，基于此类李雅普诺夫函数，开发了新的充分必要可接纳性分析条件。所呈现的结果处理具有无界变化率的时变参数，基于参数无关的 HPLF，以及通过利用多面体参数相关的 HPLF 位于多面体内部的有界变化率。在数值上，也为这两种情况推导出了易于处理的充分 LMI 条件。与文献中的结果进行了比较，