Limit Occupational Measures Set for a Control System and Averaging of Singularly Perturbed Control Systems

We discuss conditions for the existence of the limit occupational measures set for a control system. We approximate slow components of the trajectories of a singularly perturbed control system by the solutions of a differential inclusion. The differential inclusion is obtained via averaging the slow subsystem over measures from the limit occupational measures set constructed for the associated system describing the ‘‘fast’’ motions with ‘‘frozen’’ slow ones.