  We prove the existence of a compact, finite dimensional, global attractor for
a coupled PDE system comprising a nonlinearly damped semilinear wave equation
and a nonlinear system of thermoelastic plate equations, without any mechanical
(viscous or structural) dissipation in the plate component. The plate dynamics
is modelled following Berger's approach; we investigate both cases when
rotational inertia is included into the model and when it is not. A major part
in the proof is played by an estimate--known as stabilizability estimate--which
shows that the difference of any two trajectories can be exponentially
stabilized to zero, modulo a compact perturbation. In particular, this
inequality yields bounds for the attractor's fractal dimension which are
independent of two key parameters, namely $\gamma$ and $\kappa$, the former
related to the presence of rotational inertia in the plate model and the latter
to the coupling terms. Finally, we show the upper semi-continuity of the
attractor with respect to these parameters.
