Canonical realization of observers wilth arbitrarily assigned poles for linear functions of the state

Hiroyuki Kajiwara; Katsuhisa Furuta

doi:10.1080/00207177908922711

Canonical realization of observers wilth arbitrarily assigned poles for linear functions of the state

Hiroyuki Kajiwara, Katsuhisa Furuta

Ship and Marine Dynamics

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

1 Citation (Scopus)

Abstract

This paper shows that an observer Σ_ob(Â, [Bcirc], Ĉ, [Dcirc], ˆJ) for a linear function Kx of the state of a time-invariant linear system Σ(A., B, C) is characterized by a new system Σ_OB(Â, [Bcirc], Ĉ, [Dcirc]) with the initial state Ĵ which receives Markov parameters (CA^tB)_{t =0, … +μ−1}as the input and gives (KA_tB)_{t=, v+μ−1}as the output, where v is the controllability index of (A, B) and;μ is the observability index of (Â, Ĉ), It admits that the observer is constructed by a realization of σ_OB(Â, [Bcirc], Ĉ, [Dcirc]) from the input-output data and a determination of the initial state Ĵ. An algorithm is presented to construct the lower order observer with arbitrarihy assigned poles in a canonical form.

Original language	English
Pages (from-to)	457-469
Number of pages	13
Journal	International Journal of Control
Volume	29
Issue number	3
DOIs	https://doi.org/10.1080/00207177908922711
Publication status	Published - Jan 1 1979

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications

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10.1080/00207177908922711

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title = "Canonical realization of observers wilth arbitrarily assigned poles for linear functions of the state",

abstract = "This paper shows that an observer Σob({\^A}, [Bcirc], Ĉ, [Dcirc], ˆJ) for a linear function Kx of the state of a time-invariant linear system Σ(A., B, C) is characterized by a new system ΣOB({\^A}, [Bcirc], Ĉ, [Dcirc]) with the initial state Ĵ which receives Markov parameters (CAtB)t =0, … +μ−1as the input and gives (KAtB)t=, v+μ−1as the output, where v is the controllability index of (A, B) and;μ is the observability index of ({\^A}, Ĉ), It admits that the observer is constructed by a realization of σOB({\^A}, [Bcirc], Ĉ, [Dcirc]) from the input-output data and a determination of the initial state Ĵ. An algorithm is presented to construct the lower order observer with arbitrarihy assigned poles in a canonical form.",

author = "Hiroyuki Kajiwara and Katsuhisa Furuta",

year = "1979",

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N2 - This paper shows that an observer Σob(Â, [Bcirc], Ĉ, [Dcirc], ˆJ) for a linear function Kx of the state of a time-invariant linear system Σ(A., B, C) is characterized by a new system ΣOB(Â, [Bcirc], Ĉ, [Dcirc]) with the initial state Ĵ which receives Markov parameters (CAtB)t =0, … +μ−1as the input and gives (KAtB)t=, v+μ−1as the output, where v is the controllability index of (A, B) and;μ is the observability index of (Â, Ĉ), It admits that the observer is constructed by a realization of σOB(Â, [Bcirc], Ĉ, [Dcirc]) from the input-output data and a determination of the initial state Ĵ. An algorithm is presented to construct the lower order observer with arbitrarihy assigned poles in a canonical form.

AB - This paper shows that an observer Σob(Â, [Bcirc], Ĉ, [Dcirc], ˆJ) for a linear function Kx of the state of a time-invariant linear system Σ(A., B, C) is characterized by a new system ΣOB(Â, [Bcirc], Ĉ, [Dcirc]) with the initial state Ĵ which receives Markov parameters (CAtB)t =0, … +μ−1as the input and gives (KAtB)t=, v+μ−1as the output, where v is the controllability index of (A, B) and;μ is the observability index of (Â, Ĉ), It admits that the observer is constructed by a realization of σOB(Â, [Bcirc], Ĉ, [Dcirc]) from the input-output data and a determination of the initial state Ĵ. An algorithm is presented to construct the lower order observer with arbitrarihy assigned poles in a canonical form.

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