  In this paper, we consider the application of optimal periodic control
sequences to switched dynamical systems. The control sequence is obtained using
a finite-horizon optimal method based on dynamic programming. We then consider
Euler approximate solutions for the system extended with bounded perturbations.
The main result gives a simple condition on the perturbed system for
guaranteeing the existence of a stable limit cycle of the unperturbed system.
An illustrative numerical example is provided which demonstrates the
applicability of the method.
