The stability of fractional singular systems with time delay under state feedback

We discuss the stability of fractional singular systems with time delay under the state feedback. Considering the singularity of the system, we decomposed the system into two subsystems. Through fractional Laplacian transformation and inverse Laplacian transformation on the subsystems, the expression of the state variables in time domain is obtained. According to the characteristics of Mittag-Leffler function, some inequalities that have important influence on stability are derived. Finally, we find a new sufficient condition to make the fractional singular systems with time delay stable when the fractional order belongs to 1 < α < 2. Correspondingly, we can also select the appropriate state feedback matrix under the condition that make system stable. All processes are proved and numerical examples are provided to show the validity and feasibility of the proposed method.