Abstract

In this paper, a state feedback controller is designed to stabilize a class of fractional order unified systems at their unstable equilibrium points. The fractional-order chaotic Chen system is chosen to get stabilized in two cases of commensurate and incommensurate orders. An observer based technique is used to identify an unknown parameter of the unified system. The system with identified parameter is stabilized at their unstable equilibrium points using two different methods of; a classical feedback scheme and so called the enhanced one. According to the Routh-Hurwitz and relevant stability theorem for fractional system, the stability criteria are discussed whilst they are theoretically proven. Simulation results are demonstrated for the Chen system to illustrate the effectiveness of the proposed control scheme. Simulation result verifies using the proposed control technique increases the stability region of the unified fractional system regardless for commensurate or incommensurate orders. Considering the simplicity in the structure of the controller, the convergence speed is found satisfactory.

Key words: Unified chaotic system, state feedback, uncertainty principle, chaosstabilization, equilibrium points.