Global Asymptotic Stabilization of Affine Periodic Systems by Damping Control

Sufficient conditions for uniform global asymptotic stabilization of the origin by damping control are obtained for affine periodic systems. The proof is based on the use of the Krasovsky—La Salle invariance principle for periodic systems. These results generalize the Jurdjevic—Quinn Theorem to periodic systems. The corollaries for bilinear periodic control systems are obtained. It is shown that for bilinear periodic control systems the property of consistency is sufficient for existence of damping control.