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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2014

Stability of switched linear hyperbolic systems by Lyapunov techniques

Résumé

Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The dynamics and the boundary conditions are subject to abrupt changes given by a switching signal, modeled as a piecewise constant function and possibly a dwell time. By means of Lyapunov techniques some sufficient conditions are obtained for the exponential stability of the switching system, uniformly for all switching signals. Different cases are considered with or without a dwell time assumption on the switching signals, and on the number of positive characteristic velocities (which may also depend on the switching signal). Some numerical simulations are also given to illustrate some main results, and to motivate this study.
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Dates et versions

hal-00845766 , version 1 (17-07-2013)

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Christophe Prieur, Antoine Girard, Emmanuel Witrant. Stability of switched linear hyperbolic systems by Lyapunov techniques. IEEE Transactions on Automatic Control, 2014, 59 (8), pp.2196-2202. ⟨10.1109/TAC.2013.2297191⟩. ⟨hal-00845766⟩
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