Dissipation inequalities for the analysis of a class of PDEs

• Mohamadreza Ahmadi ^[1] ; Giorgio Valmorbida ^[1] ; Antonis Papachristodoulou ^[1]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 66, 2016, págs. 163-171
• Idioma: inglés
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• Resumen

  • 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.