title: Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2).
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.
authors.affiliation: College of Teacher Education, Xingtai University, Xingtai 054001, China; College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China.
authors.forename: Ruoxun
authors.initials: R
authors.lastname: Zhang
authors.affiliation: College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China.
authors.forename: Gang
authors.initials: G
authors.lastname: Tian
authors.affiliation: College of Physics Science and Information Engineering, Hebei Normal University, Shijiazhuang 050016, China. Electronic address: yangship@mail.hebtu.edu.cn.
authors.forename: Shiping
authors.initials: S
authors.lastname: Yang
authors.affiliation: Department of physics, Shijiazhuang College, Shijiazhuang 050001, China.
authors.forename: Hefei
authors.initials: H
authors.lastname: Cao
keywords: Fractional order nonlinear system; Linear state feedback controller; Stability