Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems

被引：0

作者：

Jiang Liu

Naijun Zhan

Hengjun Zhao

机构：

[1] Chinese Academy of Sciences,Chongqing Institute of Green and Intelligent Technology

[2] State Key Laboratory of Computer Science,undefined

[3] Institute of Software,undefined

[4] Chinese Academy of Sciences,undefined

[5] State key Laboratory of Computer Science,undefined

[6] Institute of Software,undefined

[7] University of Chinese Academy of Science,undefined

[8] Chinese Academy of Sciences,undefined

来源：

Mathematics in Computer Science | 2012年 / 6卷 / 4期

关键词：

Polynomial dynamical system; Asymptotic stability; Lyapunov function; Higher order Lie derivative; Primary 93D20; Secondary 13F20;

D O I：

10.1007/s11786-012-0133-6

中图分类号：

学科分类号：

摘要：

The notion of Lyapunov function plays a key role in the design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard Lyapunov functions to relaxed Lyapunov functions (RLFs), by considering higher order Lie derivatives. Furthermore, we present a method for automatically discovering polynomial RLFs for polynomial dynamical systems (PDSs). Our method is relatively complete in the sense that it is able to discover all polynomial RLFs with a given predefined template for any PDS. Therefore it can also generate all polynomial RLFs for the PDS by enumerating all polynomial templates.

引用

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页码：395 / 408

页数：13

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