Averaging with disturbances and closeness of solutions
The authors establish that, under appropriate conditions, the solutions to a time-varying system with disturbances converge uniformly on compact time intervals to the solutions to 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 by \textit{D. Nešić} and \textit{A. R. Teel} [Input-to-state stability for nonlinear time-varying systems via averaging, Math. Control Signals Syst. 14, No. 3, 257-280 (2001; Zbl 0997.93088); see also: On averaging and the ISS property, Proceedings of the 38th Conference on Decision and Control, Phoenix, AZ, December 1999, 3346-3351 (1999)].
scientific article; zbMATH DE number 1493466