On the existence of homoclinic orbits in n-dimensional piecewise affine systems

Based on the mathematical analysis of the stable manifolds, unstable manifolds and solutions of subsystems, this paper provides methodologies to ensure the existence of homoclinic orbits (degenerate and non-degenerate) which cross the switching manifold transversally at two points in n-dimensional two-zone piecewise affine systems. In addition, two examples are provided to illustrate the effectiveness of the methods, moreover, the simulation results of homoclinic orbits and chaotic invariant sets are provided for the two examples.