Dissipation inequalities for the analysis of a class of PDEs

被引：37
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
收藏
页码：163 / 171
页数：9
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