Brief paper: Averaging techniques without requiring a fast time-varying differential equation

Authors:
Joan Peuteman;Dirk Aeyels
Affiliations:
Katholieke Hogeschool Brugge Oostende, Departement IW&T, lab ECOREA, Zeedijk 101, Oostende B-8400, Belgium;SYSTeMS Research Group, Universiteit Gent, Technologiepark 914, B-9042 Zwijnaarde, Belgium
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

An averaging result is presented for local uniform asymptotic stability of nonlinear differential equations without requiring a fast time-varying vectorfield. The nonlinearity plays a crucial role: close to the origin, the trajectories vary slowly compared to the time dependence of the vectorfield. The result generalises averaging results which prove stability properties for systems having a homogeneous vectorfield with positive order. The result is illustrated with several examples.