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Article . 1978
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SIAM Journal on Control and Optimization
Article . 1978 . Peer-reviewed
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Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions

Function space controllability of linear retarded systems: a derivation from abstract operator conditions
Authors: Manitius, A.; Triggiani, R.;

Function Space Controllability of Linear Retarded Systems: A Derivation from Abstract Operator Conditions

Abstract

Controllability of linear retarded systems is investigated by using the abstract representation of such systems given by $\dot x = \tilde Ax + \tilde Bu$, where x belongs to Hilbert space $R^n \times L_2 ([ - h,0],R^n )$ denoted as $M_2 $, and $\tilde A$ generates a $C_0 $-semigroup. It is shown that useful, practically verifiable conditions can be obtained by this approach.The following problems are investigated: approximate controllability in the space $M_2 $ and its subspace, $L_2 $, exact Euclidean $(R^n )$ controllability, spectral controllability, feedback stabilizability and a relation between pointwise degeneracy and function space controllability. Starting from the abstract functional analytic framework, the analysis is carried down to the matrix theory level, through the crucial intermediate role of the theory of entire functions.

Keywords

Controllability, Control problems for functional-differential equations, function space controllability, approximate controllability, feedback, spectral controllability, linear retarded systems, Groups and semigroups of linear operators, Linear systems in control theory, Stabilization of systems by feedback, Control/observation systems in abstract spaces

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
107
Top 10%
Top 1%
Top 10%
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