LMI-Based Stability of Nonlinear Non-Autonomous Fractional-Order Systems With Multiple Time Delays

Abstract

Linear matrix inequality (LMI), as a class of stability conditions for non-autonomous fractional-order (NAFO) systems, is proposed in this paper. Based on the fractional-order Lyapunov direct method, the Mittag-Leffler stability of fractional-order systems without time delay is analyzed under LMI conditions first. For fractional-order systems with multiple time delays, the LMI conditions of Lyapunov asymptotical stability are studied by using the fractional-order comparison principle. Besides, the stability of linear NAFO systems is analyzed by using the LMI approach. What is more, the LMI-based stability method of nonlinear NAFO systems with multiple time delays is presented. Especially, for nonlinear fractional-order systems, a sufficient condition of the existence and uniqueness of the equilibrium point is given in the LMI form. In addition, two examples are provided to verify the effectiveness of the obtained theoretical results.