Robust admissibility and H∞ performance of time-varying descriptor systems

This paper addresses the problems of admissibility and H_∞ performance analysis for continuous-time linear time-varying (LTV) descriptor systems. Firstly, necessary and sufficient conditions are proposed to ascertain the admissibility of LTV descriptor systems based on the Lyapunov theory. Secondly, admissibility and H_∞ performance analysis results are derived to deal with linear parameter-varying descriptor systems, where the parameters and their time-derivatives are supposed to be bounded with known limits. These results are then cast in terms of parameter-dependent strict linear matrix inequalities (LMIs) considering affine and polynomial parameter-dependent Lyapunov functions. A numerical example illustrates the proposed approach.