Equivalence of discretizations of analog controllers

Guofeng Zhang; Xiang Chen; Tongwen Chen

doi:10.3182/20080706-5-KR-1001.2052

Equivalence of discretizations of analog controllers

Guofeng Zhang, Xiang Chen, Tongwen Chen

Research output: Chapter in book / Conference proceeding › Conference article published in proceeding or book › Academic research › peer-review

1 Citation (Scopus)

Abstract

This paper first introduces the fractional-order hold transformation that, together with the generalized bilinear transformation recently proposed in Zhang et al. [2007], contains all commonly used discretization methods as special cases. In light of this, it further shows that at fast sampling, all the digital approximations of an analog controller are equivalent in the sense of $ell-p$ induced norm for $pin [1, infty]$ when the analog controller is stable or in the sense of some gap metric even when it is unstable.

Original language	English
Title of host publication	Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC
Volume	17
Edition	1 PART 1
DOIs	https://doi.org/10.3182/20080706-5-KR-1001.2052
Publication status	Published - 1 Dec 2008
Event	17th World Congress, International Federation of Automatic Control, IFAC - Seoul, Korea, Republic of Duration: 6 Jul 2008 → 11 Jul 2008

Conference

Conference	17th World Congress, International Federation of Automatic Control, IFAC
Country/Territory	Korea, Republic of
City	Seoul
Period	6/07/08 → 11/07/08

Keywords

Digital implementation
Stability of hybrid systems
Time-varying systems

ASJC Scopus subject areas

Control and Systems Engineering

More information

10.3182/20080706-5-KR-1001.2052

Cite this

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title = "Equivalence of discretizations of analog controllers",

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keywords = "Digital implementation, Stability of hybrid systems, Time-varying systems",

author = "Guofeng Zhang and Xiang Chen and Tongwen Chen",

year = "2008",

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AB - This paper first introduces the fractional-order hold transformation that, together with the generalized bilinear transformation recently proposed in Zhang et al. [2007], contains all commonly used discretization methods as special cases. In light of this, it further shows that at fast sampling, all the digital approximations of an analog controller are equivalent in the sense of $ell-p$ induced norm for $pin [1, infty]$ when the analog controller is stable or in the sense of some gap metric even when it is unstable.

KW - Digital implementation

KW - Stability of hybrid systems

KW - Time-varying systems

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U2 - 10.3182/20080706-5-KR-1001.2052

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M3 - Conference article published in proceeding or book

SN - 9783902661005

VL - 17

BT - Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC

T2 - 17th World Congress, International Federation of Automatic Control, IFAC

Y2 - 6 July 2008 through 11 July 2008

ER -

Equivalence of discretizations of analog controllers

Abstract

Conference

Keywords

ASJC Scopus subject areas

More information

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