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 is the third and final component of a three-part effort onobservers contracting a Riemannian distance between the state of the system andits estimate. In Part I, we showed that such a contraction property holds ifthe system dynamics and the Riemannian metric satisfy two key conditions: adifferential detectability property and a geodesic monotonicity property. Withthe former condition being the focus of Part II, in this Part III, we study thelatter condition in relationship to the nullity of the second fundamental formof the output function. We formulate sufficient and necessary conditions for itto hold. We establish a link between it and the infinite gain margin property,and we provide a systematic way for constructing a metric satisfying thiscondition. Finally, we illustrate cases where both conditions hold and proposeways to facilitate the satisfaction of these two conditions together.

Convergence of Nonlinear Observers on R^n with a Riemannian Metric (Part III)