On the existence of homoclinic orbits in some class of three-dimensional piecewise affine systems

In this paper, we investigate a class of three-dimensional piecewise affine systems with the matrix in each subsystem processing a pair of complex eigenvalues and a real eigenvalue. Furthermore, we obtain some sufficient and necessary conditions for the existence of homoclinic orbits under suitable assumptions. Finally, some concrete examples are presented to illustrate our results.