Robust S-regularity of matrix pencils applied to the analysis of descriptor models

This paper deals with the robust S-regularity of an uncertain linear matrix pencil Eλ-A and its applicability to the analysis of uncertain linear descriptor models of the form (for the continuous case) or Exk+1=Axk (for the discrete case). LMI (Linear Matrix Inequality)-based conditions for the robust S-regularity of Eλ-A are established when both A and E are affected by LFT (Linear Fractional Transform)-based uncertainties. These conditions, though sufficient, are also necessary in numerous cases of practical interest. Moreover, the relevance of the conditions for the analysis of the D-admissibility of descriptor models (D-stability and impulse freeness or causality) is also discussed.