English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper proposes several Converse Lyapunov Theorems for nonlineardynamical systems defined on smooth connected Riemannian manifolds andcharacterizes properties of corresponding Lyapunov functions in a normalneighborhood of an equilibrium. We extend the methods of constructing ofLyapunov functions for ordinary differential equations on $\mathds{R}^{n}$ todynamical systems defined on Riemannian manifolds by employing the differentialgeometry. By employing the derived properties of Lyapunov functions, weobtained the stability of perturbed dynamical systems on Riemannian manifolds.The results are obtained by employing the notions of normal neighborhoods, theinjectivity radius on Riemannian manifolds and existence of bump functions onmanifolds.

A Local Characterization of Lyapunov Functions and Robust Stability of Perturbed Systems on Riemannian Manifolds