Two-time-scale distributions and singular perturbations

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) singular...

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Bibliographic Details
Main Authors: Oloomi, H.M., Sarhangi, G.R., Najafi, M.
Format: Conference Proceeding
Language:English
Subjects:
Educational institutions
Frequency domain analysis
Hydrogen
Laplace equations
Speech synthesis
State-space methods
Transfer functions
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Summary: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 decompositions of singularly perturbed systems and also the frequency domain decompositions 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/sub 1/ norm.< >
DOI:10.1109/CDC.1994.411738