Stabilization of Unstable Fixed Points of Fractional-Order Systems by Fractional-Order Linear Controllers and Its Applications in Suppression of Chaotic Oscillations

Abstract

In this paper, two fractional-order linear controllers are proposed to stabilize unstable equilibrium points of a chaotic fractional-order system. The first controller is based on the dynamic output feedback control idea and requires detectability of the linearized model of the fractional-order system on the equilibrium point. The second controller is a dynamic state feedback controller and requires observability of the linearized model. In both considered cases, the stabilizability of the model is assumed. The number of inner states in the second controller is one and therefore its structure is much simpler than the first controller. To illustrate the applicability, these controllers are applied to control chaos in the fractional-order Chen system. Numerical simulations results are presented to evaluate the performance of the proposed controllers.