Geometric properties of solution of a cylindrical dynamic system with impulsive state feedback control. (February 2015)

• Record Type: Journal Article
• Authors: Guo, Hongjian; Chen, Lansun; Song, Xinyu
• Is Part Of: Nonlinear analysis. Volume 15(2015)
• Page Start: 98
• Page End: 111
• Publication Date: 2015-02
• Subjects: Cylindrical dynamic system -- State feedback control -- Impulsive effect -- Geometric property; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2014.08.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: A kind of cylindrical dynamic system with impulsive state feedback control is formulated and investigated. Based on the qualitative properties of the corresponding continuous system, the existence of order- k ( k ∈ Z + ) periodic solutions of the cylindrical dynamic system with impulsive state feedback control is discussed on the cylinder with perimeter 2 π . If the equilibrium of the corresponding continuous system in the rectangle coordinate system is an unstable node, then the cylindrical dynamic system has two one-side stable minimum limit sets. If the equilibrium is an unstable focus, then, for different parameters, the cylindrical dynamic system has the periodic solutions with different periods and different orders. Finally, numerical simulations are given to verify the theoretical results.