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

Christophe Prieur (1) , Frédéric Mazenc (2, 3)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 L2S - Laboratoire des signaux et systèmes

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.

Domaines: Automatique / Robotique; Optimisation et contrôle [math.OC]

Christophe Prieur, Frédéric Mazenc. ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws. Mathematics of Control, Signals, and Systems, 2012, 24 (1), pp.111-134. ⟨10.1007/s00498-012-0074-2⟩. ⟨hal-00682443⟩