ISS Lyapunov functions for time-varying hyperbolic partial differential equations

Christophe Prieur, Frederic Mazenc
2011 IEEE Conference on Decision and Control and European Control Conference  
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 with a function which is a weak Lyapunov function in some cases, but is not in others. We transform this function through a strictification approach which gives a time-varying strict Lyapunov function which allows
more » ... s to establish asymptotic stability in the general case and a robustness property with respect to additive disturbances of Input-to-State Stability (ISS) type. Christophe Prieur is with Department of Automatic Control, Gipsa-lab,
doi:10.1109/cdc.2011.6160401 dblp:conf/cdc/PrieurM11 fatcat:xkr3hwogczhyrlami2fcjirjsq