On the Conditions for Invariance of the Sets Belonging to the Phase Portraits of Nonlinear Dynamic Systems

Authors:
V. P. Zhukov
Affiliations:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Venue:
Automation and Remote Control
Year:
2005

Citing 2
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Abstract

Consideration was given to the conditions for invariance of the sets belonging to the phase portraits of the nonlinear dynamic systems, that is, to the conditions under which these sets consist of entire trajectories of the dynamic systems following nonlinear autonomous vector ordinary differential equations of an arbitrary order. The necessary and sufficient conditions for invariance of the phase sets as well as the sufficient conditions for nonexistence of the invariant sets were presented.