Quiver Semistability and Structured Kalman Decompositions for Networked Linear Dynamical Systems
Abstract
We introduce new notions of controllability and observability for networked linear time-invariant (LTI) systems based on σ-semistability of quiver representations. Utilizing King's criterion for σ-semistability, we define a network generalization of the Kalman decomposition for networked LTI systems, which systematically decomposes the local and interconnection dynamics while respecting the underlying network structure. Furthermore, we present efficient algorithms for deciding the proposed controllability and observability of a given networked LTI system and for finding the Kalman-type decomposition. We also show efficient algorithms for deciding the σ-semistability of representations of acyclic quivers with self-loops if the weight σ has the same sign for all vertices with self-loops. Such quiver representations and weights arise from networked LTI systems.
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BibTeX
@misc{murota2026quiver,
title = {{Quiver Semistability and Structured Kalman Decompositions for Networked Linear Dynamical Systems}},
author = {Kazuo Murota and Tasuku Soma},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29871},
eprint = {2608.29871},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29871},
}
RIS
TY - UNPB
TI - Quiver Semistability and Structured Kalman Decompositions for Networked Linear Dynamical Systems
AU - Kazuo Murota
AU - Tasuku Soma
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29871
UR - https://arxiv.org/abs/2608.29871
AB - We introduce new notions of controllability and observability for networked linear time-invariant (LTI) systems based on σ-semistability of quiver representations. Utilizing King's criterion for σ-semistability, we define a network generalization of the Kalman decomposition for networked LTI systems, which systematically decomposes the local and interconnection dynamics while respecting the underlying network structure. Furthermore, we present efficient algorithms for deciding the proposed controllability and observability of a given networked LTI system and for finding the Kalman-type decomposition. We also show efficient algorithms for deciding the σ-semistability of representations of acyclic quivers with self-loops if the weight σ has the same sign for all vertices with self-loops. Such quiver representations and weights arise from networked LTI systems.
ER -