Dissipation inequalities for the analysis of a class of PDEs

被引：38

作者：

Ahmadi, Mohamadreza ^{[1
]}

Valmorbida, Giorgio ^{[1
]}

Papachristodoulou, Antonis ^{[1
]}

机构：

[1] Univ Oxford, Dept Engn Sci, Parks Rd, Oxford OX1 3PJ, England

来源：

AUTOMATICA | 2016年 / 66卷

基金：

英国工程与自然科学研究理事会;

关键词：

Distributed parameter systems; Convex optimization; Sum-of-squares programming; Dissipation inequalities; Interconnected systems; LYAPUNOV FUNCTIONS; STABILITY; SYSTEMS; STABILIZATION;

D O I：

10.1016/j.automatica.2015.12.010

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we develop dissipation inequalities for a class of well-posed systems described by partial differential equations (PDEs). We study passivity, reachability, induced input-output norm boundedness, and input-to-state stability (ISS). We consider both cases of in-domain and boundary inputs and outputs. We study the interconnection of PDE-PDE systems and formulate small gain conditions for stability. For PDEs polynomial in dependent and independent variables, we demonstrate that sum-of-squares (SOS) programming can be used to compute certificates for each property. Therefore, the solution to the proposed dissipation inequalities can be obtained via semi-definite programming. The results are illustrated with examples. (C) 2016 The Authors. Published by Elsevier Ltd.

引用

页码：163 / 171

页数：9