Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems

被引：7

作者：

Liu, Jiang ^{[1
]}

Zhan, Naijun ^{[2
]}

Zhao, Hengjun ^{[3
]}

机构：

[1] Chinese Acad Sci, Chongqing Inst Green & Intelligent Technol, Bldg B,Hon Kwow Ctr 85 Jinyu Ave,North Zone, Chongqing 401122, Peoples R China

[2] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China

[3] Univ Chinese Acad Sci, Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China

来源：

MATHEMATICS IN COMPUTER SCIENCE | 2012年 / 6卷 / 04期

关键词：

Polynomial dynamical system; Asymptotic stability; Lyapunov function; Higher order Lie derivative;

D O I：

10.1007/s11786-012-0133-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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

页码：395 / 408

页数：14