Optimal periodic systems of control with singular perturbations

A method is suggested for an asymptotic solution of the problem of the synthesis of an optimal periodic control of a singularly perturbed linear periodic system at an integral quadratic performance criterion. The periodic problem that arises in this case for the singularly perturbed matrix Riccati differential equation reduces to the initial problem for a lower-dimensional matrix equation without singular perturbations. Examples of the periodic vibration control of mechanical systems are considered.