Stability and stabilization of nonlinear fractional-order systems by Lyapunov direct approach

This paper focuses on the stability and stabilization problems of nonlinear fractional-order systems with fractional-order : 0 <; α <; 1. A sufficient condition for the stability and stabilization of nonlinear fractional-order systems is presented by Lyapunov direct approach. All results are obtained in term of linear matrix inequalities (LMI). Finally, two numerical examples are given to demonstrate the validity of the proposed approach.