Limit Cycle Generation for Multi-Modal and 2-Dimensional Piecewise Affine Control Systems

This paper considers a limit cycle control problem of a multi-modal and 2-dimensional piecewise affine control system. Limit cycle control means a controller design method to generate a limit cycle for given piecewise affine control systems. First, we deal with a limit cycle synthesis problem and derive a new solution of the problem. In addition, theoretical analysis on the rotational direction and the period of a limit cycle is shown. Next, the limit cycle control problem for piecewise affine control system is formulated. Then, we obtain matching conditions such that the piecewise affine control system with the state feedback law corresponds to the reference system which generates a desired limit cycle. Finally, in order to indicate the effectiveness of the new method, a numerical simulation is illustrated.