Derivation And Mathematical Analysis Of Piecewise Affine Oscillators With Desired Polygonal Limit Cycles

This study is devoted to derivation and mathematical analysis of piecewise affine oscillators that have desired polygonal limit cycles. First, a design method of a piecewise affine oscillator from data of a polygonal closed curve to be a desired limit cycle is developed. Next, a mathematical guarantee on existence, uniqueness, and stability of the limit cycle is proven. In addition, some properties for limit cycle solution trajectories of the piecewise affine oscillator are investigated. As a result, a numerical simulation shows that the piecewise affine oscillator has a unique and stable limit cycle and it is equal to the desired polygonal closed curve.