Robust stability analysis of fractional-order uncertain singular nonlinear system with external disturbance

This paper investigates robust stability for fractional-order (FO) singular nonlinear systems. The FO system is disturbed by external uncertainty and disturbance. A central analysis technique is enabled by proposing a fundamental boundedness lemma, for the first time. This lemma is used for robust stability analysis of FO systems, especially for Mittag-Leffler stability analysis of FO nonlinear systems. More importantly, how to obtain a more accurate bound is given to reduce conservative. An FO proportional-derivative (PD) controller is proposed to normalize the FO singular system. Furthermore, a criterion for stability of the normalized FO nonlinear systems is provided by linear matrix inequalities (LMIs). Finally, two illustrative simulation examples are presented to illustrate effectiveness of the proposed stability notion.