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

Abstract : 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.
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https://hal.inria.fr/hal-01214441
Contributor : Pierre-Olivier Lamare Connect in order to contact the contributor
Submitted on : Monday, October 12, 2015 - 12:08:51 PM
Last modification on : Tuesday, October 19, 2021 - 11:22:23 PM
Long-term archiving on: : Thursday, April 27, 2017 - 12:17:52 AM

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  • HAL Id : hal-01214441, version 1

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Pierre-Olivier Lamare, Antoine Girard, Christophe Prieur. Numerical Computation of Lyapunov Function for Hyperbolic PDE using LMI Formulation and Polytopic Embeddings. LPVS 2015 - 1st IFAC Workshop on Linear Parameter Varying Systems, Oct 2015, Grenoble, France. ⟨hal-01214441⟩

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