Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems

被引：0
|
作者：
Abate, Matthew [1 ,2 ]
Klett, Corbin [3 ]
Coogan, Samuel [2 ,4 ]
Feron, Eric [3 ]
机构：
[1] Georgia Inst Technol, Sch Mech Engn, Atlanta, GA 30332 USA
[2] Georgia Inst Technol, Sch Elect & Comp Engn, Atlanta, GA 30332 USA
[3] Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA
[4] Georgia Inst Technol, Sch Civil & Environm Engn, Atlanta, GA 30332 USA
来源：
2020 AMERICAN CONTROL CONFERENCE (ACC) | 2020年
关键词：
D O I：
10.23919/acc45564.2020.9147662
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic Lyapunov functions for a related hierarchy of Lyapunov differential equations. This creates an intuitive procedure for checking the stability properties of switched linear systems, and a computationally competitive algorithm is presented for generating high-order homogeneous polynomial Lyapunov functions in this manner. Additionally, we provide a comparison between polynomial Lyapunov functions generated with our proposed approach and Lyapunov functions generated with a more traditional sum-of-squares based approach.
引用
收藏
页码：5322 / 5327
页数：6
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