Averaging techniques without requiring a fast time-varying differential equation

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....

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Bibliographic Details
Published in:Automatica (Oxford) 2011-01, Vol.47 (1), p.192-200
Main Authors: Peuteman, Joan, Aeyels, Dirk
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic properties
Asymptotic stability
Automation
Averaging
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Differential equations
Exact sciences and technology
Lyapunov
Nonlinearity
Origins
Stability
Time dependence
Time-varying
Trajectories
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2010.10.039