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Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2)
Ruoxun Zhang1, Gang Tian2, Shiping Yang2
1College of Teacher Education, Xingtai University, Xingtai 054001, China; College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China.
Abstract:
This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 <α<2. By using the Mittag-Leffler function, Laplace transform and the Gronwall-Bellman lemma, one sufficient condition is attained for the local asymptotical stability of a class of fractional order nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.
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