ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws

  • Christophe PrieurEmail author
  • Frédéric Mazenc
Original Article


A family of time-varying hyperbolic systems of balance laws is considered. The partial differential equations of this family can be stabilized by selecting suitable boundary conditions. For the stabilized systems, the classical technique of construction of Lyapunov functions provides a function which is a weak Lyapunov function in some cases, but is not in others. We transform this function through a strictification approach to obtain a time-varying strict Lyapunov function. It allows us to establish asymptotic stability in the general case and a robustness property with respect to additive disturbances of input-to-state stability (ISS) type. Two examples illustrate the results.


Strictification Lyapunov function Hyperbolic PDE System of balance laws 


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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of Automatic ControlGipsa-labGrenoble CedexFrance
  2. 2.Team INRIA DISCO, L2S, CNRS-SupelecGif-sur-YvetteFrance

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