In this paper we study exact boundary controllability for a system of two linear wave equations coupled by lower order terms. We obtain square integrable control of Neuman type for initial state with finite energy, in nonsmooth domains of the plane. PreliminariesLet Ω ⊂ R 2 be a bounded simply connected domain with piecewise C ∞ boundary ∂Ω. It is assumed that ∂Ω has no cuspid points and that Ω lays in one side of ∂Ω. We will refer to this type of domain as curvilinear polygon. The exterior unit normal vector η is defined almost everywhere in ∂Ω. Points of R 2 × R are denoted by (x 1 , x 2 , t), denotes the Laplacian operator in the spatial variable x = (x 1 , x 2 ) ∈ R 2 and subscripts are used for partial derivatives. Consider the systemwith T > 0, α, β, γ , δ real constants and ∂Ω = Γ 0 ∪ Γ 1 is a decomposition of the boundary where the parts Γ 0 and Γ 1 have disjoint interiors but their closure may have common isolated points. Many problems in structural dynamics are modeled by this type of system. For instance, the equations (1.2) describe the transverse free vibrations of an elastically connected double-membrane compound system. In this case u and v are the displacements of two vibrating membranes measured from their equilibrium positions. The coupling terms ±α(u − v) represent forces imposed by the coupling elastic layer. If the membranes are held fixed on the portion Γ 0 of the * Corresponding author.

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In this work we study exact boundary controllability for a class of hyperbolic linear partial differential equation with constant coefficient which includes the linear Klein-Gordon equation. We consider piecewise smooth domains on the plane, initial state with finite energy and control of Robin type, acting on the whole boundary or only on a part of it.