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 |
|---|---|
| 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 | |
| State | Published - Dec 1 1997 |
| Externally published | Yes |
Fingerprint
Keywords
- Delta operator
- Fixed point arithmetic
- Limit cycles
- Quantization error
ASJC Scopus subject areas
- Electrical and Electronic Engineering
Cite this
Limit cycles in delta-operator formulated 1-d and m-d discrete-time systems with fixed-point arithmetic. / Bauer, Peter H.; Premaratne, Kamal.
In: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 44, No. 6, 01.12.1997, p. 529-537.Research output: Contribution to journal › Article
}
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
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 -