Abstract
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.
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