Stabilization of generalized fractional order chaotic systems using state feedback control

In this paper, we address the problem of chaos control of three types of fractional order systems using simple state feedback gains. Electronic chaotic oscillators, mechanical "jerk" systems, and the Chen system are investigated when they assume generalized fractional orders. We design the static gains to place the eigenvalues of the system Jacobian matrices in a stable region whose boundaries are determined by the orders of the fractional derivatives. We numerically demonstrate the effectiveness of the controller in eliminating the chaotic behavior from the state trajectories, and driving the states to the nearest equilibrium point in the basin of attraction. For the recently introduced Chen system, in particular, we demonstrate that with a proper choice of model parameters, chaotic behavior is preserved when the system order becomes fractional. Both state and output feedback controllers are then designed to stabilize a generalized fractional order Chen system.