Stability and Stabilization of Kronecker-Sum-Coupled Multilinear Systems
Abstract
Coupled dynamical systems with multi-dimensional state structures arise in many applications such as spatiotemporal processes and large-scale interconnected systems. However, existing studies primarily focus on matrix-based coupled systems or tensor-based dynamical systems without couplings. The properties of coupled tensor-based systems remain largely unexplored. In this article, we study Kronecker-sum-coupled multilinear systems under the transform-based tensor product framework. We establish fundamental tensor spectral properties showing that stability can be characterized through lower-dimensional subsystem dynamics together with slice-wise matrix stability in the transform domain. We further develop optimization conditions for state-feedback stabilization and show that the stabilization problem can be decomposed into independent subsystem problems. Finally, we analyze the computational complexity of the proposed framework and demonstrate its substantial computational advantages over unfolding-based approaches using both synthetic systems and multi-inertia motor systems.
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BibTeX
@misc{he2026stability,
title = {{Stability and Stabilization of Kronecker-Sum-Coupled Multilinear Systems}},
author = {Ziqin He and Ruoying Wang and Shenghan Mei and Yidan Mei and Xin Mao and Can Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25529},
eprint = {2610.25529},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25529},
}
RIS
TY - UNPB
TI - Stability and Stabilization of Kronecker-Sum-Coupled Multilinear Systems
AU - Ziqin He
AU - Ruoying Wang
AU - Shenghan Mei
AU - Yidan Mei
AU - Xin Mao
AU - Can Chen
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25529
UR - https://arxiv.org/abs/2610.25529
AB - Coupled dynamical systems with multi-dimensional state structures arise in many applications such as spatiotemporal processes and large-scale interconnected systems. However, existing studies primarily focus on matrix-based coupled systems or tensor-based dynamical systems without couplings. The properties of coupled tensor-based systems remain largely unexplored. In this article, we study Kronecker-sum-coupled multilinear systems under the transform-based tensor product framework. We establish fundamental tensor spectral properties showing that stability can be characterized through lower-dimensional subsystem dynamics together with slice-wise matrix stability in the transform domain. We further develop optimization conditions for state-feedback stabilization and show that the stabilization problem can be decomposed into independent subsystem problems. Finally, we analyze the computational complexity of the proposed framework and demonstrate its substantial computational advantages over unfolding-based approaches using both synthetic systems and multi-inertia motor systems.
ER -