A limit cycle synthesis method of multi-modal and 2-dimensional piecewise affine systems

This paper is devoted to a synthesis problem of a multi-modal and 2-dimensional piecewise affine system that generates a desired stable limit cycle. By using the proposed synthesis method, we can obtain a multi-modal and 2-dimensional piecewise affine system from given data on a desired limit cycle trajectory. In addition, the existence and the uniqueness of desired stable limit cycle for the obtained system can be proven. It also turns out that we can determine the rotation direction and the period of the limit cycle by adjusting the parameters of the system. In order to show the effectiveness of our new synthesis method, we illustrate various simulation results.