Dissipation inequalities for the analysis of a class of PDEs
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 input...
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| Veröffentlicht in: | Automatica (Oxford) 2016-04, Vol.66, p.163-171 |
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| container_title | Automatica (Oxford) |
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| creator | Ahmadi, Mohamadreza Valmorbida, Giorgio Papachristodoulou, Antonis |
| description | 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. |
| doi_str_mv | 10.1016/j.automatica.2015.12.010 |
| format | Article |
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| ispartof | Automatica (Oxford), 2016-04, Vol.66, p.163-171 |
| issn | 0005-1098 1873-2836 |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Automatic Boundaries Convex optimization Dissipation Dissipation inequalities Distributed parameter systems Engineering Sciences Inequalities Interconnected systems Norms Partial differential equations Polynomials Programming Stability Sum-of-squares programming |
| title | Dissipation inequalities for the analysis of a class of PDEs |
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