Estimation of domain of attraction for the fractional-order WPT system

Abstract This paper investigates the problem of domain of attraction of the fractional-order wireless power transfer (WPT) system. As a fractional-order piecewise affine system, firstly, the model of the fractional-order WPT system is established. Secondly, based on the Lyapunov function approach and the inductive method, sufficient conditions of the boundedness for the fractional-order WPT system and the fractional-order system with periodically intermittent control are derived, respectively. In the meantime, the relevant inequality technique is introduced so as to decrease the conservatism of the results. The derived results can be used for estimating the domain of attraction of the systems. Finally, several examples are given to demonstrate the obtained results. Simulation shows that the conservatism of the results is indeed reduced in theory, and the designed controller is effective.