  We study stability of abstract differential equations coupled by means of a
general algebraic condition. Our approach is based on techniques from operator
theory and systems theory, and it allows us to study coupled systems by
exploiting properties of the components, which are typically much simpler to
analyse. As our main results we establish resolvent estimates and decay rates
for abstract boundary-coupled systems. We illustrate the power of the general
results by using them to obtain rates of energy decay in coupled systems of
one-dimensional wave and heat equations, and in a wave equation with an
acoustic boundary condition.
