Realizations of perturbations of an observable pair with prescribed indices - Beitia, M.A.; Compta, A.; Hoyos, I.; Peña, M. (Linear algebra and its applications, 2011)
It is well known that, when a full rank observable pair (C,A) is slightly perturbed, the new observability indices k′ are majorized by the initial ones k, k≻k′. Conversely, any indices k′ majorized by k can be obtained by perturbing (C,A). The aim of this paper is the explicit construction of perturbations of (C,A) which have the desired indices k′ by means of a sequence of uniparametrical versal perturbations. Even more, using versal deformations we refine this construction in such a way that the perturbation has the maximum possible number of zeros and no parameters in the square part.