  In this paper we study the stability properties of strongly continuous
semigroups generated by block operator matrices. We consider triangular and
full operator matrices whose diagonal operator blocks generate polynomially
stable semigroups. As our main results, we present conditions under which also
the semigroup generated by the operator matrix is polynomially stable. The
theoretic results are applied to deriving conditions for the polynomial
stability of a system consisting of a two-dimensional and a one-dimensional
damped wave equations.
