Homogeneous polynomial Lyapunov functions for the admissibility analysis of uncertain descriptor systems

This paper addresses the admissibility analysis of uncertain time-varying continuous-time descriptor systems. The results proposed in our paper extend the stability analysis approach based on homogeneous polynomial Lyapunov functions (HPLFs) previously developed for uncertain standard state-space systems to the robust admissibility analysis of uncertain descriptor ones. A new power transformation of the state vector with respect to its dynamic and algebraic parts has been proposed leading to new LMI admissibility analysis conditions. These conditions are less restrictive than the ones based on quadratic Lyapunov functions as sustained by our numerical examples.