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

Pierre-Olivier Lamare 1 Antoine Girard 1 Christophe Prieur 2
2 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
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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Pierre-Olivier Lamare, Antoine Girard, Christophe Prieur. Numerical Computation of Lyapunov Function for Hyperbolic PDE using LMI Formulation and Polytopic Embeddings. 1st IFAC Workshop on Linear Parameter Varying Systems (LPVS 2015 ), Oct 2015, Grenoble, France. ⟨hal-01214441⟩

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