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arXiv · 2105.00968

Perturbation-Tolerant Structural Controllability for Linear Systems

Yuan Zhang·Yuanqing Xia·Gang Wang·Jinhui Zhang
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Abstract

This paper proposes a notion termed perturbation-tolerant structural controllability (PTSC) to study the generic property of controllability preservation/resilience of structured linear systems under structured perturbations. A structured system is said to be PTSC with respect to a perturbation structure if for almost all controllable realizations of this system, there are no complex-valued perturbations obeying the zero/nonzero pattern prescribed by the perturbation structure that can make the perturbed systems uncontrollable. We prove a generic property in this notion, that for almost all controllable realizations of a structured system, either there exist such structured perturbations rendering the systems uncontrollable, or there are no such perturbations. We present a decomposition-based necessary and sufficient condition for the PTSC of single-input linear systems, whose verification has polynomial time complexity. We then discuss some intuitive graph-theoretic conditions for PTSC. As an application, our results can serve as some feasibility conditions for the conventional structured controllability radius problems from a generic viewpoint.

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Yuan Zhang, Yuanqing Xia, Gang Wang, Jinhui Zhang. 2021-05-03. Perturbation-Tolerant Structural Controllability for Linear Systems. https://doi.org/10.1109/tac.2024.3351558

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