Numerical Computation of Lyapunov Function for Hyperbolic PDE using LMI Formulation and Polytopic Embeddings^*

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• 作者：Pierre-Olivier Lamare^* ; ^{pierre-olivier.lamare@imag.fr" class="auth_mail" title="E-mail the corresponding author} ; Antoine Girard^* ; ^{antoine.girard@imag.fr" class="auth_mail" title="E-mail the corresponding author} ; Christophe Prieur^** ; ^{christophe.prieur@gipsa-lab.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hyperbolic PDE ; Lyapunov method ; LMI
• 刊名：IFAC-PapersOnLine
• 出版年：2015
• 出版时间：2015
• 年：2015
• 卷：48
• 期：26
• 页码：7-12
• 全文大小：428 K

文摘

We consider the problem of stability analysis and control synthesis for first-order hyperbolic linear PDEs over a bounded interval with spatially varying coefficients. We propose LMI-based conditions for the stability and for the design of boundary and distributed control for this class of systems. These LMI-based conditions involve an infinite number of LMI. Hence, we show how to overapproximate these constraints using polytopic embeddings to reduce the problem to a finite number of LMI. We show the effectiveness of the overapproximation with several examples.