Abstract: Stability is the foundation of analysis and design of the control systems. To explore the stability conditions of the fractional-order systems, especially fractional-order nonlinear delayed systems, is one of the most difficult issues in the field of the control theory and engineering. This paper is concerned with stability and stabilization of a class of fractional-order nonlinear delayed systems. By transforming the systems into an equivalent fractional integral ones and using inequality scaling technique, a new effective sufficient stability condition with simple form is established for such systems. Based on the proposed the results, some stabilization criteria are also derived by designing time-delay linear feedback controller. Finally, a numerical example illustrates the effectiveness of the results. In addition, the proposed methods are also extended and applied to other type fractional-order systems.

Key words: fractional-order systems, stability, stabilization, nonlinear systems, linear feedback controller