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Linear feedback : an algebraic approach

By MLJ Malo Hautus and M Heymann


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:
Provided by: Repository TU/e
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