Averaging with disturbances and closeness of solutions

摘要

We establish that, under appropriate conditions, the solutions of a time-varying system with disturbances converge uniformly on compact time intervals to the solutions of the system's average as the rate of change of time increases to infinity. The notions of "average" used for systems with disturbances are the "strong" and "weak" averages introduced in Nesic and Teel (D. Nesic, A.R. Teel, Input-to-state stability for time-varying nonlinear systems via averaging, 1999, submitted for publication. See also: On averaging and the ISS property, Proceedings of the 38th Conference on Decision and Control, Phoenix, AZ, December 1999, pp. 3346-3351.) (C) 2000 Elsevier Science B.V. All rights reserved. [References: 9]