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.
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