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 < α ≤ 1 and with order 1 ≤ β < 2, one may
get more relevant theorems. Finally, two examples are provided to
demonstrate the effectiveness of our results.
Abstract: In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.