کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10413116 895495 2005 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the realization of periodic functions
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
On the realization of periodic functions
چکیده انگلیسی
In this article, canonical and spectrally minimal infinite-dimensional state space realizations for periodic functions are considered. It is shown that the periodic functions having ℓ1 Fourier coefficients are precisely those realizable by a Riesz spectral system (RSS) in which the system operator generates a periodic strongly continuous semigroup and the observation operator is bounded. This realization can easily be converted to a canonical and spectrally minimal form. It is shown how the use of RSS and Cesáro sums of Fourier series allows the construction of a state space realization for a given periodic function merely integrable over its period. Simple finite-dimensional approximations with error bounds are derived for the RSS realization. Regular well-posed linear systems (WPLS) are used to construct a Fuhrmann-type realization for a given periodic function integrable over its period. It is shown that the RSS realizations and WPLS realizations are precisely equally good at coping with the possible ill behavior of a given bounded periodic function integrable over its period, but the WPLS realization is not always spectrally minimal or canonical.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Systems & Control Letters - Volume 54, Issue 3, March 2005, Pages 225-235
نویسندگان
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