New approach to asymptotic stability: time-varying nonlinear systems

L. T. Grujić

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-20

Abstract:

The results of the paper concern a broad family of time-varying nonlinear systems with differentiable motions. The solutions are established in a form of the necessary and sufficient conditions for: 1) uniform asymptotic stability of the zero state, 2) for an exact single construction of a system Lyapunov function and 3) for an accurate single determination of the (uniform) asymptotic stability domain. They permit arbitrary selection of a function p ( ⋅ ) from a defined functional family to determine a Lyapunov function v ( ⋅ ) , [ v ( ⋅ ) ] , by solving v ′ ( ⋅ ) = − p ( ⋅ ) {or equivalently, v ′ ( ⋅ ) = − p ( ⋅ ) [ 1 − v ( ⋅ ) ] }, respectively. Illstrative examples are worked out.

Date: 1997
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/20/529147.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/20/529147.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:529147

DOI: 10.1155/S016117129700046X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().