Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic

Peter H. Bauer; Kamal Premaratne

doi:10.1109/81.586026

Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic

Peter H. Bauer, Kamal Premaratne

Research output: Contribution to journal › Article

1 Scopus citations

Abstract

In this paper, the problem of global asymptotic stability of δ-operator formulated one-dimensional (1-D) and multidimensional (m-D) discrete-time systems is analyzed for the case of fixed point implementations. It is shown that the free response of such a system tends to produce improper equilibrium points if conventional quantization arithmetic schemes such as truncation or rounding are used. Explicit necessary conditions for global asymptotic stability are derived in terms of the sampling period. These conditions demonstrate that, in many cases, fixed-point arithmetic does not allow for global asymptotic stability in δ-operator formulated discrete-time systems that use a short sampling period. This is true for the 1-D as well as the m-D case.

Original language	English (US)
Pages (from-to)	529-537
Number of pages	9
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	44
Issue number	6
DOIs	https://doi.org/10.1109/81.586026
State	Published - Dec 1 1997
Externally published	Yes

Keywords

Delta operator
Fixed point arithmetic
Limit cycles
Quantization error

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/81.586026

Fingerprint Dive into the research topics of 'Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic'. Together they form a unique fingerprint.

Cite this

Bauer, P. H., & Premaratne, K. (1997). Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 44(6), 529-537. https://doi.org/10.1109/81.586026

@article{5ebaeff0e5474d00bd87b830932b6d0f,

title = "Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic",

abstract = "In this paper, the problem of global asymptotic stability of δ-operator formulated one-dimensional (1-D) and multidimensional (m-D) discrete-time systems is analyzed for the case of fixed point implementations. It is shown that the free response of such a system tends to produce improper equilibrium points if conventional quantization arithmetic schemes such as truncation or rounding are used. Explicit necessary conditions for global asymptotic stability are derived in terms of the sampling period. These conditions demonstrate that, in many cases, fixed-point arithmetic does not allow for global asymptotic stability in δ-operator formulated discrete-time systems that use a short sampling period. This is true for the 1-D as well as the m-D case.",

keywords = "Delta operator, Fixed point arithmetic, Limit cycles, Quantization error",

author = "Bauer, {Peter H.} and Kamal Premaratne",

year = "1997",

month = dec,

day = "1",

doi = "10.1109/81.586026",

language = "English (US)",

volume = "44",

pages = "529--537",

journal = "IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications",

issn = "1057-7122",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "6",

}

TY - JOUR

T1 - Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic

AU - Bauer, Peter H.

AU - Premaratne, Kamal

PY - 1997/12/1

Y1 - 1997/12/1

N2 - In this paper, the problem of global asymptotic stability of δ-operator formulated one-dimensional (1-D) and multidimensional (m-D) discrete-time systems is analyzed for the case of fixed point implementations. It is shown that the free response of such a system tends to produce improper equilibrium points if conventional quantization arithmetic schemes such as truncation or rounding are used. Explicit necessary conditions for global asymptotic stability are derived in terms of the sampling period. These conditions demonstrate that, in many cases, fixed-point arithmetic does not allow for global asymptotic stability in δ-operator formulated discrete-time systems that use a short sampling period. This is true for the 1-D as well as the m-D case.

AB - In this paper, the problem of global asymptotic stability of δ-operator formulated one-dimensional (1-D) and multidimensional (m-D) discrete-time systems is analyzed for the case of fixed point implementations. It is shown that the free response of such a system tends to produce improper equilibrium points if conventional quantization arithmetic schemes such as truncation or rounding are used. Explicit necessary conditions for global asymptotic stability are derived in terms of the sampling period. These conditions demonstrate that, in many cases, fixed-point arithmetic does not allow for global asymptotic stability in δ-operator formulated discrete-time systems that use a short sampling period. This is true for the 1-D as well as the m-D case.

KW - Delta operator

KW - Fixed point arithmetic

KW - Limit cycles

KW - Quantization error

UR - http://www.scopus.com/inward/record.url?scp=0031162996&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031162996&partnerID=8YFLogxK

U2 - 10.1109/81.586026

DO - 10.1109/81.586026

M3 - Article

AN - SCOPUS:0031162996

VL - 44

SP - 529

EP - 537

JO - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

JF - IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

SN - 1057-7122

IS - 6

ER -