A New Limit Cycle Control Method for Multi-modal and 2-dimensional Piecewise Affine Control Systems via State Feedback

The aim of this study is to develop a new limit cycle control method for multi-modal and 2-dimensional piecewise affine control systems via state feedback. Especially, the study focuses on relaxation of design conditions shown in the authors’ previous work by adding a new free parameter. First, matching conditions such that the closed-loop system is equivalent to the reference system with a desired limit cycle are derived. Then, the analytic solution and its existence conditions are shown by solving the matching conditions. A numerical simulation shows that the new control method can generate a desired limit cycle for a given system.