A (Strongly) Connected Weighted Graph is Uniformly Detectable based on any Output Node
Systems and Control
2022-09-28 v1 Systems and Control
Dynamical Systems
Abstract
Many dynamical systems, including thermal, fluid, and multi-agent systems, can be represented as weighted graphs. In this paper we consider whether the unstable states of such systems can be observed from limited discrete-time measurement, that is, whether the discrete formulation of system is detectable. We establish that if the associated graph is fully connected, then a linear time invariant system is detectable by measuring any state. Further, we show that a parameter-varying or time-varying system remains uniformly detectable for a reasonable approximation of its state transition matrix, if the underlying graph structure is maintained.
Keywords
Cite
@article{arxiv.2209.13119,
title = {A (Strongly) Connected Weighted Graph is Uniformly Detectable based on any Output Node},
author = {Uduak Inyang-Udoh and Michael Shanks and Neera Jain},
journal= {arXiv preprint arXiv:2209.13119},
year = {2022}
}