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

Author

Bauer, Peter H. ; Premaratne, Kamal

Author_Institution

Dept. of Electr. Eng., Notre Dame Univ., IN, USA

Volume

44

Issue

6

fYear

1997

fDate

6/1/1997 12:00:00 AM

Firstpage

529

Lastpage

537

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

asymptotic stability; digital arithmetic; discrete time systems; limit cycles; multidimensional systems; quantisation (signal); delta-operator formulation; discrete-time systems; equilibrium points; fixed-point arithmetic; free response; global asymptotic stability; limit cycles; multidimensional systems; one-dimensional systems; quantization arithmetic schemes; sampling period; Asymptotic stability; Bandwidth; Convergence; Discrete time systems; Fixed-point arithmetic; Floating-point arithmetic; Limit-cycles; Multidimensional systems; Quantization; Sampling methods;

fLanguage

English

Journal_Title

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

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.586026

Filename

586026