Limit cycle synthesis of multi-modal and 2-dimensional piecewise affine systems

In this paper, we develop a synthesis method for a multi-modal and 2-dimensional piecewise affine system that generates a desired stable limit cycle. By using the synthesis method, we can design a multi-modal and 2-dimensional piecewise affine system from the given data on a desired limit cycle trajectory. Moreover, we prove that the obtained system has a unique and stable limit cycle and it corresponds to the desired limit cycle trajectory. It also turns out that the rotation direction and the period of the limit cycle can be controlled by changing the parameters in the system. Some simulation results show the effectiveness of our new synthesis method.

► A limit cycle synthesis method for piecewise affine systems is provided.
► The existence and uniqueness of the limit cycle for the system is proved.
► We analyze rotational directions and periods for limit cycles of the system.
► The effectiveness of our new method is verified via various numerical examples.