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On the representation of linear system half‐line maps
Author(s) -
Sandberg Irwin W.
Publication year - 2005
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.319
Subject(s) - impulse response , bounded function , integrable system , convolution (computer science) , mathematics , limit (mathematics) , linear system , impulse (physics) , expression (computer science) , representation (politics) , invariant (physics) , transfer function , function (biology) , pure mathematics , discrete mathematics , computer science , mathematical analysis , engineering , artificial intelligence , physics , electrical engineering , quantum mechanics , evolutionary biology , politics , artificial neural network , political science , law , mathematical physics , biology , programming language
An expression is given for the most general input–output map associated with the members of a certain important large family of causal linear shift‐invariant systems with bounded inputs. This expression is a function‐space limit of a convolution. Also given is a necessary and sufficient condition under which the limit can be written as a convolution with an integrable impulse‐response function. Related material concerning engineering education, as well as additional results for other sets of inputs, is also given. Copyright © 2005 John Wiley & Sons, Ltd.