Research ArticleStability analysis of a class of fractional order nonlinear systems with order lying in (0, 2)

- Stability of a class of fractional order nonlinear systems with order lying in (0, 2) has been investigated.
- One sufficient condition is attained for the local asymptotical stability of a class of fractional order nonlinear systems with order lying in (0, 2).
- The obtained results can be applied to stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller.

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.