Criteria of Kalman's Type to the Approximate Controllability and the Approximate Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls

Abstract

In this paper the authors obtain necessary conditions, presented as criteria of Kalman's type, to the approximate null controllability, the approximate synchronization, and the approximate synchronization by groups, respectively, for a coupled system of wave equations with Dirichlet boundary controls. The sufficiency of these conditions is also established for $N\times N$ cascade systems, for some $2\times 2$ systems, as well as for diagonalizable systems in the one-space-dimensional case.