This paper proposes a novel state-dependent switched energy function (SdSEF) for general nonlinear autonomous systems

and constructs an SdSEF for doubly-fed induction generator (DFIG)-based wind power generation systems (WPGSs). Different from the conventional energy function

SdSEF is a piece-wise continuous function

and it satisfies the conditions of conventional energy functions on each of its continuous segments. SdSEF is designed to bridge the gap between the well-developed energy function theory and the description of system energy of complex nonlinear systems

such as power electronics converter systems. The stability criterion of nonlinear autonomous systems is investigated with SdSEF

and mathematical proof is presented. The SdSEF of a typical DFIG-based WPGS is simulated in the whole processes of a grid fault and fault recovery. Simulation results verify the negativeness of the derivative of each continuous segment of the SdSEF.