Finite-time Bounded Tracking Control for Fractional-order Systems

This paper solves the finite-time bounded tracking control problem for fractional-order systems. Firstly, by taking the fractional derivative on state equations and error signals, a fractional-order error system is constructed, and the error signal is taken as the output vector of the error system. Secondly, a state feedback controller is introduced into the error system, and the disturbance signal of the error system is the combination of the fractional derivative of disturbance signals and desired tracking signals. Thus, the original problem is converted into the input-output finite time stability problem of the closed-loop error systems. Thirdly, based on the linear matrix inequalities (LMIs), the sufficient conditions which ensure the finite-time bounded tracking for the desired tracking signals are derived. Therefore, the finite-time bounded tracking controller of the original system is obtained. Finally, simulation results elucidate the effectiveness of the controller.