Dilated LMI conditions for the robust analysis of uncertain parameter-dependent descriptor systems

This paper addresses the robust admissibility/ℌ
₂
performance analysis for continuous-time uncertain parameter-dependent descriptor systems. In order to achieve less conservative results, the proposed approach uses parameter-dependent Lyapunov functions and slack variables. Our main contribution consists in proposing new necessary and sufficient conditions for the admissibility and ℌ
₂
performance analysis of time-invariant singular systems. These conditions are formulated as a strict linear matrix inequality (LMI) solvability problem and represent a generalization to singular systems of some dilated LMI analysis results developed in the literature for state-space systems. Also, we have extended our results to the analysis of descriptor systems with time-varying parametric uncertainties. A numerical example shows the applicability of our approach.