Studying on the stability of fractional-order nonlinear system

In this paper, we study the properties of the Mittag–Leffler function and propose an approach for calculating the maximum norm of eigenvalue of Jacobian matrix of nonlinear system. Then a simple approach is proposed for judging the stability of fractional nonlinear system. Based on the approach, the maximum decay rate of fractional nonlinear system can be calculated. Finally, some examples are provided to illustrate the approach.

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