Observability properties for discrete conservative systems

Spectral characterisations of Observability properties for discrete conservative systems

Recently, we have obtained in a joint work with Chuang Zheng and Enrique Zuazua a sharp observability results for time-discrete abstract schemes,using a new approach based on a resolvent estimate characterization of the observability. This result is very general and decouples the problems related to the time-discretization method and to the space-approximation scheme.

Following this idea, we have then developed several spectral criteria of observability for conservative systems to adapt this new technique to space discrete methods. Again, this will yield very general results for the observability of waves and Schrödinger systems. However, the optimality of our results are not obvious at all. I will explain this issue precisely.

I will then discuss several open problems related to these questions.