  It is rigorously proved that the chaotic dynamics of the non-smooth system
with relay function is persistent even if a chaotic perturbation is applied. We
consider chaos in a modified Li-Yorke sense such that infinitely many almost
periodic motions take place in its basis. It is demonstrated that the system
under investigation possesses countable infinity of chaotic sets of solutions.
Coupled Duffing oscillators are used to show the effectiveness of our
technique, and simulations that support the theoretical results are
represented. Moreover, a chaos control procedure based on the Ott-Grebogi-Yorke
algorithm is proposed to stabilize the unstable almost periodic motions
embedded in the chaotic attractor.
