Admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties

This paper investigates the admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties. Firstly, based on the analysis of the regularity, causality and stability, novel admissibility conditions for nominal fractional-order singular discrete systems are derived including a necessary and sufficient condition in terms of spectral radius and a sufficient condition in terms of non-strict linear matrix inequalities. In order to eliminate the coupling terms and propose strict linear matrix inequality results, another novel admissibility condition is obtained, which is more tractable and reliable with the available linear matrix inequality software solver and more suitable for the controller design compared with the existing results. Secondly, the state feedback controller synthesis for the fractional-order singular discrete systems with interval uncertainties is addressed and the state feedback controller is designed. Finally, the efficiency of the proposed method is demonstrated by two numerical simulation examples.