کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7155648 1462623 2015 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems
ترجمه فارسی عنوان
با استفاده از توابع لایپونوف درجه دوم به منظور ثابت کردن ثبات یکنواخت لیاپانوف برای سیستم های مرتبه کسر
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
چکیده انگلیسی
This paper presents two new lemmas related to the Caputo fractional derivatives, when α∈0,1, for the case of general quadratic forms and for the case where the trace of the product of a rectangular matrix and its transpose appear. Those two lemmas allow using general quadratic Lyapunov functions and the trace of a matrix inside a Lyapunov function respectively, in order to apply the fractional-order extension of Lyapunov direct method, to analyze the stability of fractional order systems (FOS). Besides, the paper presents a theorem for proving uniform stability in the sense of Lyapunov for fractional order systems. The theorem can be seen as a complement of other methods already available in the literature. The two lemmas and the theorem are applied to the stability analysis of two Fractional Order Model Reference Adaptive Control (FOMRAC) schemes, in order to prove the usefulness of the results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 22, Issues 1–3, May 2015, Pages 650-659
نویسندگان
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