On Averaging Technique for Nonlinear Time-Varying Systems without Local Lipschitz Continuity

Abstract

The majority of literature for averaging methods deal with a class of nonlinear time-varying (NLTV) dynamics and their time-invariant averaged systems with locally Lipschitz continuous (LLC) condition. In this work, a class of uniformly continuous NLTV systems and their uniformly continuous averaged systems are considered. The first result shows the closeness of solutions between the original NLTV system and its averaged system with a sufficiently small time-scale separation parameter ε on a subset of a time interval, in which both systems have well-defined solutions. If the averaged system is finite-time stable (FTS), the second result shows that the original NLTV system will uniformly converge to an arbitrarily small neighborhood of the origin on a finite-time interval with sufficiently small ε. Simulation results support the theoretical finding.