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Linear feedback : an algebraic approach

By MLJ Malo Hautus and M Heymann

Abstract

The algebraic theory of linear input–output maps is reexamined with the objective of accomodating the concept of (state) feedback in this theory. The concepts of extended and restricted linear i/o maps (and linear i/s maps) are introduced and investigated. It is shown how fraction representations of transfer matrices arise naturally in this new theoretical framework.Conditions are given for when the change caused to a linear input-output map by an (open loop) cascade compensator can also be accomplished by utilization of (closed loop) state feedback. In particular, it is shown that the change caused to a linear input-output map by cascading (composing) it with an input space isomorphism, can also be effected by feedback, provided the input space isomorphism in bicausal , i.e. it does not change the causal structure of the input-output map. Further detailed characterizations of feedback are also given especially in connection with the newly introduced concepts of degree chain and degree list

Publisher: Society for Industrial and Applied Mathematics (SIAM)
Year: 1978
OAI identifier: oai:library.tue.nl:681983
Provided by: Repository TU/e
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