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In this paper a novel switching control strategy for suppressing undesired limit cycles in autonomous smooth and non-smooth systems is presented. The switching controller is designed by using the theory of non-smooth bifurcations. Namely, a nearby corner-collision event introduced by the switching control law is used to suppress the unwanted oscillatory motion and introduce a desired stable equilibrium point. The switching control action is only started when the system trajectories enter an appropriately defined corner region in phase space including the desired equilibrium point. The technique is proven to be effective in the case of three different representative examples.