810 research outputs found

    A new H2-norm Lyapunov function for the stability of a singularly perturbed system of two conservation laws

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    International audienceIn this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H2-norm for a singularly perturbed system of conservation laws is constructed. It is based on the Lyapunov functions of two subsystems in L2-norm

    Boundary Observers for Linear and Quasi-linear Hyperbolic Systems with Application to Flow Control

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    International audienceIn this paper we consider the problem of boundary observer design for one-dimensional fi rst order linear and quasi-linear strict hyperbolic systems with n rightward convecting transport PDEs. By means of Lyapunov based techniques, we derive some su fficient conditions for exponential boundary observer design using only the information from the boundary control and the boundary conditions. We consider static as well as dynamic boundary controls for the boundary observer design. The main results are illustrated on the model of an inviscid incompressible flow

    Dynamic Boundary Stabilization of First Order Hyperbolic Systems

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    International audienceIn this chapter, we address the problem of the dynamic boundary stabilization of linear, quasilinear and LPV first-order hyperbolic systems. We provide sufficient conditions for the exponential stability for this class of infinite dimensional systems by means of Lyapunov based techniques and matrix inequalities. We develop an applicative example of a temperature boundary control in a Poiseuille flow using some of our main results and we present simulation results that illustrate the efficiency of our approach

    Boundary Feedback Control for Hyperbolic Systems

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    We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems Rd\mathbb{R}^d. Using a novel Lyapunov function taking into account the multi-dimensional geometry we show stabilization in L2L^2 for the arising system using a suitable feedback control. We show the applicability discussing the barotropic Euler equations.Comment: arXiv admin note: text overlap with arXiv:2207.1200
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