Title :
Two-time-scale distributions and singular perturbations
Author :
Oloomi, Hossein M. ; Sarhangi, G. Reza ; Najafi, Mahmoud
Author_Institution :
Dept. of Eng., Purdue Univ., Fort Wayne, IN, USA
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 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 L1 norm
Keywords :
Laplace transforms; frequency-domain analysis; large-scale systems; singularly perturbed systems; time-domain analysis; transfer functions; transient response; frequency domain decompositions; impulse response; singular perturbations; stable singularly perturbed system; stable systems; time domain decomposition; transfer function; two-frequency-scale Laplace transform; two-time-scale distributions; Educational institutions; Frequency domain analysis; Hydrogen; Laplace equations; Speech synthesis; State-space methods; Transfer functions;
Conference_Titel :
Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on
Conference_Location :
Lake Buena Vista, FL
Print_ISBN :
0-7803-1968-0
DOI :
10.1109/CDC.1994.411738
