Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative

Abstract In this paper, we define a characteristic equation of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative. At the same time, by applying the Laplace transform and matrix theory we give a necessary and sufficient stability condition and some brief sufficient stability conditions. The proposed method is quite different from the other in the literature. In addition, we provide some examples to demonstrate the effectiveness of our results.