Admissibility and robust stabilization of fractional-order derivative uncertain linear continuous singular systems

Abstract

This paper focuses on the admissibility and robust stabilization conditions for fractional order singular systems with uncertainties in fractional-order derivative term. The singular system with uncertainties can be transformed into systems without uncertainties by some specific matrix transformations. Sufficient and necessary conditions are proposed to ensure that the considered closed system and open system are admissible and robust stabilization respectively. The criteria for admissibility and robust stabilization of fractional singular systems with order 0 < a < 1 which are derived in terms of linear matrix inequalities (LMIs) can be used to design controller to guarantee the closed-systems stabilizable. Finally, numerical examples are presented to illustrate the effectiveness of the criteria.