Existence of an observation window of finite width for continuous-time autonomous nonlinear systems

TL;DR

This paper investigates observability in continuous-time nonlinear systems, establishing conditions under which a finite observation window exists and constructing a related K-function, thus advancing understanding of system observability.

Contribution

It proves that systems observable via distinguishability and rank condition admit a finite observation window and constructs a corresponding K-function.

Findings

Existence of finite observation window for certain nonlinear systems

Construction of a K-function related to observability

Link between different notions of observability in nonlinear systems

Abstract

In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous nonlinear system that is observable in both distinguishability and rank condition sense permits an observation window of finite width, and it is possible to construct a K-function related to observability for such system.