Semi-global Practical Stability of Periodic Time-Varying Systems via Averaging: A Lyapunov Approach

This paper considers semi-global practical stability of a general time-varying, parameter dependent nonlinear system. A Lyapunov result for uniform semi-global practical stability of such a system is given. This sufficient condition is applied to a periodically time-varying system in the standard averaging form to obtain a sufficient condition on the averaged system for the time-varying system to be uniformly semi-globally practically stable. The sufficient condition requires the existence of a Lyapunov function that guarantees the semi-global practical stability of the averaged system, and is thus weaker than previous averaging based stability results which require the equilibrium of the averaged system to be exponentially or asymptotically stable. The proof is based on Lyapunov techniques, and does not depend on classical averaging results