New results on stability and stabilization of a class of nonlinear fractional-order systems. (English) Zbl 1283.93138
Summary: The asymptotic stability and stabilization problem of a class of fractional-order nonlinear systems with Caputo derivative are discussed in this paper. By using of Mittag-Leffler function, Laplace transform, and the generalized Gronwall inequality, a new sufficient condition ensuring local asymptotic stability and stabilization of a class of fractional-order nonlinear systems with fractional-order \(\alpha:1<\alpha<2\) is proposed. Then a sufficient condition for the global asymptotic stability and stabilization of such system is presented firstly. Finally, two numerical examples are provided to show the validity and feasibility of the proposed method.
MSC:
| 93C10 | Nonlinear systems in control theory |
| 93D20 | Asymptotic stability in control theory |
| 26A33 | Fractional derivatives and integrals |
| 93B52 | Feedback control |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
Keywords:
fractional-order systems; stability; stabilization; nonlinear systems; linear feedback controlSoftware:
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