The existence and stability analyses of periodic orbits in 3-dimensional piecewise affine systems

This paper investigates the existence and stability of periodic orbits in a class of 3-dimensional piecewise affine systems with two zones. Two results on the existence of periodic orbits are obtained by applying some fixed points theorems to a Poincaré map. Precisely, we prove the existence of a periodic sink in one case and a periodic saddle in another case. Finally, some concrete examples are given to illustrate the main results.