An invariance principle for time-varying systems

In this paper we propose an invariance principle for time-varying dynamical systems. We first present a novel proof of the Krasovskii-Lasalle invariance principle for forward time using invariance properties of regions of attraction, rather than the invariance property of the limit set. We then propose an invariance principle for bounded time-varying systems, in the spirit of the classical result, by using the Lasalle-Yoshizawa theorem and a uniformity condition. The simple, practical use of the theorem is shown using an example of a pendulum with time-varying parameters.