Continuously Equivalent State Variable Realizations

Brian D.O. Anderson

doi:10.1109/TCT.1972.1083451

Continuously Equivalent State Variable Realizations

Brian D.O. Anderson^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose one is given two minimal realizations of the same transfer function matrix. The question is asked: When does there exist a family of coordinate transformations defined by a set of nonsingular matrices T(λ), continuously dependent on λ, with T(0) = I and with T(1) mapping the state vector associated with one minimal realization into the state vector associated with the other? The quesion is answered, and a procedure is given for constructing the family when it exists.

Original language	English
Pages (from-to)	286-287
Number of pages	2
Journal	IEEE Transactions on Circuit Theory
Volume	19
Issue number	3
DOIs	https://doi.org/10.1109/TCT.1972.1083451
Publication status	Published - May 1972
Externally published	Yes

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10.1109/TCT.1972.1083451

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title = "Continuously Equivalent State Variable Realizations",

abstract = "Suppose one is given two minimal realizations of the same transfer function matrix. The question is asked: When does there exist a family of coordinate transformations defined by a set of nonsingular matrices T(λ), continuously dependent on λ, with T(0) = I and with T(1) mapping the state vector associated with one minimal realization into the state vector associated with the other? The quesion is answered, and a procedure is given for constructing the family when it exists.",

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AB - Suppose one is given two minimal realizations of the same transfer function matrix. The question is asked: When does there exist a family of coordinate transformations defined by a set of nonsingular matrices T(λ), continuously dependent on λ, with T(0) = I and with T(1) mapping the state vector associated with one minimal realization into the state vector associated with the other? The quesion is answered, and a procedure is given for constructing the family when it exists.

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Continuously Equivalent State Variable Realizations

Abstract

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