The state of dynamical input-output systems as an operator
type: Item
instance of: scholarly article
title: The state of dynamical input-output systems as an operator
zbMATH Open document ID: 0910.93008
author: William L. Root
author: Demetrios Serakos
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-04-19T00:00:00Z
review text: A causal input-output system operating for all time from the indefinite past to the indefinite future may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. The state of such a system at any instant is defined here as an operator from the space of possible future inputs to that of future outputs. This operator is called the natural state. The output space is taken to be a time-shift-invariant normed linear function space, and the input space is either also such a space or a time-shift-invariant subset thereof. There is flexibility allowed in the choice of these spaces. Both the input-output operator and the operator giving the natural state are themselves taken to be elements of normed linear spaces with one of a particular family of norms called \(N\)-power norms. The general development applies to nonlinear and time-varying systems. Continuity and boundedness of the natural state (as an operator) and properties of the natural state and its trajectory as related to the input-output description of the system are investigated. Two examples are presented.
Mathematics Subject Classification ID: 93A99
Mathematics Subject Classification ID: 93B28
zbMATH DE Number: 1218645
zbMATH Keywords: state operator
zbMATH Keywords: \(N\)-power norms
zbMATH Keywords: causal input-output system
zbMATH Keywords: nonlinear and time-varying systems
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6017
OpenAlex ID: W2094034360
cites work: Q5616462
cites work: Q5638871
cites work: Q4100575
cites work: Linear Automaton Transformations
cites work: Considerations regarding input and output spaces for time-varying dynamical systems
cites work: Q4204049
DOI: 10.1006/JMAA.1998.6017
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description: scientific article; zbMATH DE number 1218645