کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5011469 | 1462595 | 2017 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Computation of non-monotonic Lyapunov functions for continuous-time systems
ترجمه فارسی عنوان
محاسبه توابع لیپانوف غیر مونوتونی برای سیستمهای مداوم
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی مکانیک
چکیده انگلیسی
In this paper, we propose two methods to compute non-monotonic Lyapunov functions for continuous-time systems which are asymptotically stable. The first method is to solve a linear optimization problem on a compact and bounded set. The proposed linear programming based algorithm delivers a CPA1 non-monotonic Lyapunov function on a suitable triangulation covering the given compact and bounded set excluding a small neighbourhood of the equilibrium. It is shown that for every asymptotically stable system there exists a suitable triangulation such that the proposed algorithm terminates successfully. The second method is to verify a CPA function constructed based on the values of the norm of the state at all vertices of a suitable triangulation covering the given compact and bounded set is a non-monotonic Lyapunov function on the given set without a small neighbourhood of the equilibrium. It is further proved that if system is asymptotically stable then there exists a suitable triangulation such that the second way works. The comparison of the proposed two methods are discussed via three examples.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 50, September 2017, Pages 35-50
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 50, September 2017, Pages 35-50
نویسندگان
Huijuan Li, AnPing Liu,