PTSC：数值摄动下结构能控性的一种新定义
PTSC: a New Definition for Structural Controllability under Numerical Perturbations
摘要：
针对一类单输入结构化系统，提出了结构化数值扰动下的结构能控性的新概念，即扰动容限结构能控性（PTSC），该系统的输入项可分为三类：固定零项、值固定但未知的未知类元和可取任意复值的扰动项.这样的系统是PTSC，如果对于参数空间中的未知通用条目的几乎所有值，相应的可控系统实现可以在任意复值扰动下保持可控性，其结构由扰动条目规定。这一新概念可以刻画结构化数值扰动下能控性保持的通有性质。给出了单输入系统为PTSC的充要条件，其验证具有多项式时间复杂度。我们的结果可以作为一些可行性条件，从一般的角度来看，传统的结构可控性半径问题。
英文摘要：
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.
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