  Discrete-time systems cannot be passive unless there is a direct feedthrough
from the input to the output. For passivity-based control to be exploited
nevertheless, some authors introduce virtual outputs, while others rely on
continuous-time passivity and then apply discretization techniques that
preserve passivity in discrete time. Here we argue that quadratic supply rates
incorporate and extend the effect of virtual outputs, allowing one to exploit
dissipativity properties directly in discrete time. We derive decentralized
(Q,S,R)-dissipativity conditions for a set of nonlinear systems interconnected
with arbitrary topology, so that the overall network is guaranteed to be
stable. For linear systems, we develop dissipative control conditions that are
linear in the supply rate matrices. To demonstrate the validity of our methods,
we provide numerical examples in the context of islanded microgrids.
