کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
717055 892232 2013 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Critical simple imaginary characteristic roots and invariance properties for quasipolynomials: A missing link
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
پیش نمایش صفحه اول مقاله
Critical simple imaginary characteristic roots and invariance properties for quasipolynomials: A missing link
چکیده انگلیسی

This paper addresses some properties of simple characteristic roots of quasipolynomials including commensurate delays. Although such a problem seems easy and was largely treated in the literature, to the best of the authors' knowledge, the invariance and the ultimate stability properties have not been fully investigated. In this paper, we propose a new frequency-sweeping framework, which simultaneously considers the Taylor series of the critical imaginary roots as well as the Puiseux series of singular points of the frequency-sweeping curves. Through analyzing the algebraic properties of the corresponding frequency-sweeping curves, we are able to completely characterize the invariance property of the simple imaginary roots with respect to the corresponding critical delay values. As a consequence of the invariance property, the ultimate stability property can be easily derived. Finally, as a byproduct of the approach proposed in the paper, the complete stability for time-delay systems with only simple imaginary roots can be systematically derived. Some illustrative examples complete the presentation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: IFAC Proceedings Volumes - Volume 46, Issue 3, 2013, Pages 126-131