PTSC: a New Definition for Structural Controllability under Numerical Perturbations
Abstract
This paper proposes a novel notion for structural controllability under structured numerical perturbations, namely the perturbation-tolerant structural controllability (PTSC), on a single-input structured system whose entries can be classified into three categories: fixed zero entries, unknown generic entries whose values are fixed but unknown, and perturbed entries that can take arbitrary complex values. Such a system is PTSC if, for almost all values of the unknown generic entries in the parameter space, the corresponding controllable system realizations can preserve controllability under arbitrary complex-valued perturbations with their structure prescribed by the perturbed entries. This new notion can characterize the generic property in controllability preservation under structured numerical perturbations. We give a necessary and sufficient condition for a single-input system to be PTSC, whose verification has polynomial time complexity. Our results can serve as some feasibility conditions for the conventional structured controllability radius problems from a generic view.
Cite
@article{arxiv.2103.11908,
title = {PTSC: a New Definition for Structural Controllability under Numerical Perturbations},
author = {Yuan Zhang and Yuanqing Xia},
journal= {arXiv preprint arXiv:2103.11908},
year = {2021}
}
Comments
This paper includes the proofs that were left out in a conference paper to appear in the 40th Chinese Control Conference on July 26-28, 2021 in Shanghai, China. For an expanded version of this paper, see Y.Zhang, Y.Xia, G.Wang, and J.Zhang. Perturbation-tolerant structural controllability for linear systems. arXiv preprint arXiv:2105.00968, 2021