A uniform invariance principle for periodic systems with applications to synchronization

In this paper, we propose an extension of the invariance principle, which is uniform with respect to parameter uncertainties, for the class of periodic ordinary differential equations. This extension allows the derivative of the auxiliary function V, commonly called a Lyapunov function, to be positive in some bounded sets. This important feature has the potential to simplify the problem of exhibiting a function of Lyapunov-type and allows the application of the principle in systems that cannot be treated with the conventional principle, either due to the nonexistence of a Lyapunov-type function or due to the difficulty in exhibiting it. The extension of the invariance principle is useful to obtain estimates of attractors and regions of attraction that are uniform with respect to parameters. The study of synchronization of periodic coupled systems illustrates an application of the principle.