arXiv:2403.07156 Abstract | arXiv Analytics

arXiv:2403.07156 [math.DS]Abstract References Reviews Resources

On Uniqueness of Participation Factors

Published 2024-03-11Version 1

In modal analysis and control of a nonlinear dynamical system, participation factors of state variables with respect to a mode of interest serve as pivotal tools for stability studies. Linear participation factors are uniquely determined by the mode's shape and composition, which are defined by the right and left eigenvectors of the linearized model. For nonlinear participation factors as well as five other variants of participation factors, this paper finds the sufficient conditions for them to be unique against scaling factors on the shape and composition of a mode. Besides, the similarity between the scaling factor and perturbation amplitude is also discussed.

Categories: math.DS, cs.SY, eess.SY

Keywords: uniqueness, scaling factor, nonlinear participation factors, nonlinear dynamical system, sufficient conditions

Related articles: Most relevant | Search more

arXiv:math/0303310 [math.DS] (Published 2003-03-25)

Sufficient conditions for robustness of attractors

C. A. Morales, M. J. Pacifico

arXiv:0901.2201 [math.DS] (Published 2009-01-15)

Sufficient conditions under which a transitive system is chaotic

E. Akin, E. Glasner, W. Huang, S. Shao, X. Ye

arXiv:2409.10105 [math.DS] (Published 2024-09-16)

Participation Factors for Nonlinear Autonomous Dynamical Systems in the Koopman Operator Framework

Kenji Takamichi, Yoshihiko Susuki, Marcos Netto