Dissipation inequalities for the analysis of a class of PDEs. (April 2016)

• Record Type: Journal Article
• Authors: Ahmadi, Mohamadreza; Valmorbida, Giorgio; Papachristodoulou, Antonis
• Is Part Of: Automatica. Volume 66(2016)
• Page Start: 163
• Page End: 171
• Publication Date: 2016-04
• Subjects: Distributed parameter systems -- Convex optimization -- Sum-of-squares programming -- Dissipation inequalities -- Interconnected systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2015.12.010
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: 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.