Journal
NONLINEAR DYNAMICS
Volume 75, Issue 4, Pages 633-641Publisher
SPRINGER
DOI: 10.1007/s11071-013-1091-5
Keywords
Fractional-order systems; Stability; Stabilization; Nonlinear systems; Linear feedback control
Categories
Funding
- National Natural Science Funds of China for Distinguished Young Scholar [50925727]
- National Natural Science Foundation of China [61374135]
- National Defense Advanced Research Project [C1120110004, 9140 A27020211DZ5102]
- Chinese Ministry of Education [313018]
- Fundamental Research Funds for the Central Universities [2012HGCX0003]
- Natural Science Foundation of Anhui Province [11040606M12]
- 211 project of Anhui University [KJJQ1102]
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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 < 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.
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