Perturbation-Tolerant Structural Controllability for Linear Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866911774311186432 |
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| author | Zhang, Yuan Xia, Yuanqing Wang, Gang Zhang, Jinhui |
| author_facet | Zhang, Yuan Xia, Yuanqing Wang, Gang Zhang, Jinhui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_00968 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Perturbation-Tolerant Structural Controllability for Linear Systems Zhang, Yuan Xia, Yuanqing Wang, Gang Zhang, Jinhui Optimization and Control 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. |
| title | Perturbation-Tolerant Structural Controllability for Linear Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2105.00968 |