On input/output maps for nonlinear systems via continuity in a locally convex topology

In this paper we show that the output of a nonlinear system with inputs in ( L 2[0, T]; R m ) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. T...

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Bibliographic Details
Published inSystems & control letters Vol. 24; no. 4; pp. 273 - 281
Main Authors Mazumdar, Ravi R., Kannurpatti, Raghavan, Bagchi, Arunabha
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 10.03.1995
Elsevier
Subjects
Applied sciences
Approximation
Computer science; control theory; systems
Control theory. Systems
Exact sciences and technology
Infinite-dimensional systems
Nonlinear systems
Smoothness
System theory
Infinite-dimensional systems
Approximation
Nonlinear systems
Smoothness
Hilbert space
Systems theory
Infinite dimension
Topology
Non linear system
Regularity
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Summary:In this paper we show that the output of a nonlinear system with inputs in ( L 2[0, T]; R m ) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results.
ISSN:0167-6911
1872-7956
DOI:10.1016/0167-6911(94)00031-P