Abstract
This paper presents new admissibility analysis conditions for discrete-time descriptor systems. Firstly, it proposes an extension, expressed as necessary and sufficient admissibility conditions, of admissibility criteria developed in the literature for linear time-invariant systems in order to incorporate the time-varying case. This extension exploits time-varying slack variables and uses the linear matrix inequality (LMI) formulation. Then, this extension is applied to the case of polytopic descriptor systems with bounded time-varying parameters. The use of sum of squares polynomials allows to eliminate the criteria parametric dependence and to provide new admissibility analysis conditions expressed as a LMIs feasibility problem. This new admissibility analysis result uses parameter-dependent slack variables and may be less conservative than the results already proposed in the literature as sustained by our numerical evaluation.
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