Reset control of nonlinear chaotic systems using describing function

In nonlinear systems, chaos may exsist in some's parameters and may cause some unexpected damage. This paper proposes a design method of a reset controller for nonlinear chaotic systems. We consider a plant consisting of a linear system with a nonlinear feedback element and show a condition of the parameter for which chaos controls, using describing functions of the nonlinear element and the reset controller. We apply the proposed design method of the reset controller to the forced Van der Pol equation system and show its effectiveness.