Robust state feedback admissibilisation of discrete linear polytopic descriptor systems: a strict linear matrix inequality approach

This study deals with strict linear matrix inequality (LMI)-based robust admissibility analysis and robust admissibilisation of a discrete linear descriptor system associated with pencil (E,A). Indeed, the LMI condition for nominal admissibility is linear with respect to A and also with respect to E. This linearity in E is an original issue in this study. As a consequence, parameter deflections in the entries of A but also of E can then be easily taken into account owing to polytopic description to derive strict LMI sufficient conditions for robust admissibility and robust state feedback admissibilisation. The possibility to deal with parameter uncertainty on E is one of the main contributions. It is also shown how the proposed condition can go beyond the scope of the descriptor systems and can be used to approach the very challenging problem of the static output feedback stabilisation of discrete non-descriptor models.