Controllability and observability for non-autonomous evolution equations: the averaged Hautus test

2018/02/26 by Haak, Bernhard, Hoang, Duc-Trung, Ouhabaz, El-Maati
#35Q93 #93B07 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1802.09224

Abstract

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.

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