Behavior of limit cycle for nonlinear Lur´e systems

This paper explores the robust limit cycle design for a nonlinear Lur´e problem. Considering the uncertainty for the plant transfer function, the period and amplitude of the limit cycle will change. By describing function method, the nonlinear system can be linearized. Then, the overall system can be treated as a linear system. With Barkhausen criterion, a Barkhausen characteristic polynomial is proposed in this paper. It can be found that for Barkhausen characteristic equation, as the closed-loop poles are clustered, the system is extremely sensitive to parameter´s change. A formula for the design of a robust limit cycle is shown in this paper. Also, a formula to determine the limit cycle is locally stable and unstable is also presented. Simulation example will show above-mentioned results.