کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6861260 | 675380 | 2013 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Discovering polynomial Lyapunov functions for continuous dynamical systems
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
هوش مصنوعی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
In this paper we analyze locally asymptotic stability of polynomial dynamical systems by discovering local Lyapunov functions beyond quadratic forms. We first derive an algebraizable sufficient condition for the existence of a polynomial Lyapunov function. Then we apply a real root classification based method step by step to under-approximate this derived condition as a semi-algebraic system such that the semi-algebraic system only involves the coefficients of the pre-assumed polynomial. Afterward, we compute a sample point in the corresponding semi-algebraic set for the coefficients resulting in a local Lyapunov function. Moreover, we test our approach on some examples using a prototype implementation and compare it with the generic quantifier elimination based method and the sum of squares based method. These computation and comparison results show the applicability and efficiency of our approach.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 58, November 2013, Pages 41-63
Journal: Journal of Symbolic Computation - Volume 58, November 2013, Pages 41-63
نویسندگان
Zhikun She, Haoyang Li, Bai Xue, Zhiming Zheng, Bican Xia,