Stability and Stabilization of a Class of Nonlinear Fractional-Order Systems With Caputo Derivative

Abstract

This brief discusses the stability and stabilization of a class of fractional-order nonlinear systems with Caputo derivative. On the basis of the stability theory of fractional-order linear differential equation, Mittag-Leffler function, Laplace transform, and the Gronwall inequality, two sufficient conditions are derived for the asymptotical stability of a class of fractional-order nonlinear systems with fractional-order α: 0 <; α ≤ 1 and 1 <; α <; 2, respectively. Then, two sufficient conditions for asymptotical stabilization of such fractional-order systems are obtained, in which feedback gains could be ensured by the pole placement technique. Finally, some numerical examples are provided to show the validity and feasibility of the proposed method.