  This paper proposes a novel definition for structural controllability, namely
the perturbation-tolerant structural controllability, on a structured system
whose entries can be classified into three categories: fixed zero entries,
unknown generic entries whose values are fixed but indeterminate, and perturbed
entries which can take arbitrary complex values. Such a system is
perturbation-tolerantly structurally controllable 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 a structure prescribed by the perturbed
entries. This property is shown to be generic (in the single-input case). In
this paper, we give a necessary and sufficient condition for a single-input
system to be perturbation-tolerantly structurally controllable, 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.
