Stability Analysis of Fractional Order Systems with Time Delay

Abstract

In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order $0<\alpha\leq 1$ and with order $1\leq\beta<2$, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results