stability; operator theory; eigenvalues and eigenfunctions; nonlinear systems; Koopman operator
Abstract :
[en] The global description of a nonlinear system through the linear Koopman operator leads to an efficient approach to global stability analysis. In the context of stability analysis, not much attention has been paid to the use of spectral properties of the operator. This paper provides new results on the relationship between the global stability properties of the system and the spectral properties of the Koopman operator. In particular, the results show that specific eigenfunctions capture the system stability and can be used to recover known notions of classical stability theory (e.g. Lyapunov functions, contracting metrics). Finally, a numerical method is proposed for the global stability analysis of a fixed point and is illustrated with several examples.
Disciplines :
Mathematics Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Mauroy, Alexandre ; University of California Santa Barbara > Department of Mechanical Engineering
Mezic, Igor; University of California Santa Barbara > Department of Mechanical Engineering
Language :
English
Title :
A spectral operator-theoretic framework for global stability
Publication date :
December 2013
Event name :
2013 52th IEEE Conference on Decision and Control Conference, CDC 2013
Event place :
Firenze, Italy
Event date :
10-13 Dec. 2013
Audience :
International
Journal title :
Proceedings of the IEEE Conference on Decision and Control
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