Exactly Synchronizable State and Approximate Controllability for a Coupled System of Wave Equations with Locally Distributed Controls

Abstract

For a coupled system of wave equations with locally distributed controls, we prove that the exactly synchronizable state is independent of applied controls and then can be uniquely determined by the initial data if and only if the system is not approximately controllable or, equivalently, if and only if Kalman’s rank condition (3.2) holds.