In this talk I will be interested in the stabilisation and control of wave equations in a domain with boundary. It has been known for 20 years that when the domain and the metric are smooth, the celebrated geometric control condition (any geodesic reflecting on the boundary according to geometric optics enters the control region) is equivalent to stabilisation and control. Here I will investigate the stability of this latter property with respect to rough perturbations of the metric and domain (for which the notion of geodesics is not so clear). This question leads to interesting properties for non negative measures, solutions to differential equations with continuous (or even in some sense $L^\infty$) coefficients).