This article is cited in 3 papers

Deterministic Systems

On the conditions for invariance of the sets belonging to the phase portraits of nonlinear dynamic systems

V. P. Zhukov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

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.

Presented by the member of Editorial Board: B. T. Polyak

Received: 20.04.2004

 English version: Automation and Remote Control, 2005, 66:6, 866–875

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