Lyapunov stability analysis of fractional nonlinear systems

Lyapunov direct method provides a very effective approach to analyze stability of nonlinear systems, however, the well-known Leibniz rule is not suitable for fractional derivatives. This paper deals with fractional nonlinear systems and several algebraic criteria of Mittag-Leffler and asymptotical stability are obtained by using S-procedure and analytical technique. Finally, an example is given to show that it is very convenient to check stability of practical systems by using our proposed methods.