Effect of time scales on stability of coupled systems involving the wave equation

Eduardo Cerpa (1) , Christophe Prieur (2)

1 Departamento de Matematica, Universidad Tecnica Federico Santa Maria
2 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité

This article considers systems coupling an ordinary differential equation (ODE) with a wave equation through its boundary data. The main focus is put on the role of different time scales for each equation on the stability of the coupled system. A fast wave equation coupled to an ODE is proven to be stable if each subsystem is stable. However, we show examples of stable subsystems generating an unstable full system when coupling a wave equation to a fast ODE.

Domaines: Automatique / Robotique

Eduardo Cerpa, Christophe Prieur. Effect of time scales on stability of coupled systems involving the wave equation. CDC 2017 - 56th IEEE Conference on Decision and Control, Dec 2017, Melbourne, Australia. ⟨hal-01670643⟩