Paper Info
Title
Zeros of nonlinear systems with input invariances.
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∈R) or scale-invariance (u(t)↦pu(t), p∈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∈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.
Year
DOI
Venue
2017
10.1016/j.automatica.2017.03.030
Automatica
Keywords
Field
DocType
Invariant systems,Transmission zeros,Differentiators,Adaptive systems,Nonlinear systems
Discrete mathematics,Nonlinear system,Invariant (physics),Control theory,Multiplicity (mathematics),Differential operator,Transfer function,Initial value problem,Invariant (mathematics),Mathematics,Pointwise
Journal
Volume
Issue
ISSN
81
1
0005-1098
Citations 
PageRank 
References 
0
0.34
3
Authors
2
Name
Order
Citations
PageRank
Moritz Lang100.68
Eduardo D. Sontag23134781.88