Dissipation inequalities for the analysis of a class of PDEs
Dissipation inequalities for the analysis of a class of PDEs
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DOI：
10.1016/j.automatica.2015.12.010
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发表时间：
2016-04
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影响因子：
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通讯作者：
M. Ahmadi;G. Valmórbida;A. Papachristodoulou
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文献类型：
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作者：
M. Ahmadi;G. Valmórbida;A. Papachristodoulou
本文给出了一类由偏微分方程描述的适定系统的耗散不等式。我们研究了无源性、可达性、诱导输入-输出范数有界性和输入-状态稳定性。我们考虑了域内和边界输入和输出的两种情况。我们研究了PDE-PDE系统的互连，并给出了稳定的小增益条件。对于因变量和自变量的PDEs多项式，我们证明了平方和（SOS）编程可以用于计算每个属性的证书。因此，所提出的耗散不等式的解可以通过半确定规划得到。算例说明了所得结果。
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.