Two-Time-Scale Distributions and Singular Perturbations
International Journal of Control
Taylor & Francis
Place of Publication
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.
control, two-time scale distributions, TTS
Hossein Oloomi and B. Shafai (2004).
Two-Time-Scale Distributions and Singular Perturbations. International Journal of Control.77 (11), 1040-1049. United Kingdom: Taylor & Francis.