---
res:
bibo_abstract:
- 'A nonlinear system possesses an invariance with respect to a set of transformations
if its output dynamics remain invariant when transforming the input, and adjusting
the initial condition accordingly. Most research has focused on invariances with
respect to time-independent pointwise transformations like translational-invariance
(u(t) -> u(t) + p, p in R) or scale-invariance (u(t) -> pu(t), p in R>0).
In this article, we introduce the concept of s0-invariances with respect to continuous
input transformations exponentially growing/decaying over time. We show that s0-invariant
systems not only encompass linear time-invariant (LTI) systems with transfer functions
having an irreducible zero at s0 in R, but also that the input/output relationship
of nonlinear s0-invariant systems possesses properties well known from their linear
counterparts. Furthermore, we extend the concept of s0-invariances to second-
and higher-order s0-invariances, corresponding to invariances with respect to
transformations of the time-derivatives of the input, and encompassing LTI systems
with zeros of multiplicity two or higher. Finally, we show that nth-order 0-invariant
systems realize – under mild conditions – nth-order nonlinear differential operators:
when excited by an input of a characteristic functional form, the system’s output
converges to a constant value only depending on the nth (nonlinear) derivative
of the input.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Moritz
foaf_name: Lang, Moritz
foaf_surname: Lang
foaf_workInfoHomepage: http://www.librecat.org/personId=29E0800A-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Eduardo
foaf_name: Sontag, Eduardo
foaf_surname: Sontag
bibo_doi: 10.1016/j.automatica.2017.03.030
bibo_volume: 81C
dct_date: 2017^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/00051098
dct_language: eng
dct_publisher: IFAC, the International Federation of Automatic Control@
dct_title: Zeros of nonlinear systems with input invariances@
...