CONTROLLABILITY AND OBSERVABILITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS: THE AVERAGED HAUTUS TEST

Bernhard Haak (1) , Duc-Trung Hoang (1) , El-Maati Ouhabaz (1)

1 IMB - Institut de Mathématiques de Bordeaux

We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact observability. Next, we extend this to more general class of operators under a growth condition on the associated evolution family. We give an application to the Schrödinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Bernhard Haak, Duc-Trung Hoang, El-Maati Ouhabaz. CONTROLLABILITY AND OBSERVABILITY FOR NON-AUTONOMOUS EVOLUTION EQUATIONS: THE AVERAGED HAUTUS TEST. 2018. ⟨hal-01717316v1⟩