Title

Two-Time-Scale Distributions and Singular Perturbations

Document Type

Article

Publication Date

2004

Publication Source

International Journal of Control

Volume

77

Issue

11

Inclusive pages

1040-1049

DOI

10.1080/0020717042000269613

Publisher

Taylor & Francis

Place of Publication

United Kingdom

ISBN/ISSN

00207179

Abstract

Two-time-scale (TTS) distributions are introduced. For a class of stable systems, it is shown that every TTS distribution has a two-frequency-scale (TFS) Laplace transform. Conversely, it is shown that the impulse response of any stable TFS transfer function, and hence any stable (standard) singularly perturbed system, can be characterized in terms of a stable TTS distribution. A time domain decomposition for TTS distributions is obtained which parallels the slow and fast decomposition of singularly perturbed systems and also the frequency domain decomposition of TFS transfer functions. It is shown that every stable TTS distribution can be decomposed in terms of two simpler distributions represented in two different time scales. A composite distribution is constructed from these two which approximates the TTS distribution arbitrarily closely in the L 1 norm.

Keywords

control, two-time scale distributions, TTS

Disciplines

Engineering

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Link to Original Published Item

http://dx.doi.org/10.1080/0020717042000269613