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arXiv · 2309.10753

Generalized Cactus and Structural Controllability of Switched Linear Continuous-Time Systems

Yuan Zhang·Yuanqing Xia·Aming Li
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Abstract

This paper explores the structural controllability of switched linear continuous-time systems. It first identifies a gap in the proof for a pivotal criterion for the structural controllability of switched linear systems in the literature. To address this void, we develop novel graph-theoretic concepts, such as multi-layer dynamic graphs, generalized stems/buds, and generalized cacti, and based on them, provide a comprehensive proof for this criterion. Our approach also induces a new, generalized cactus based graph-theoretic criterion for structural controllability. This not only extends Lin's cactus-based graph-theoretic condition to switched systems for the first time, but also provides a lower bound for the generic dimension of controllable subspaces.

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Yuan Zhang, Yuanqing Xia, Aming Li. 2024-05-22. Generalized Cactus and Structural Controllability of Switched Linear Continuous-Time Systems. https://arxiv.org/abs/2309.10753

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