  Passivity theory has recently contributed to developing decentralized control
schemes for large-scale systems. Many decentralized passivity-based control
schemes are designed in continuous-time. It is well-known, however, that the
passivity properties of continuous-time systems may be lost under
discretization. In this work, we present a novel stabilizing decentralized
control scheme by ensuring passivity for discrete-time systems directly and
thus avoiding the issue of passivity preservation. The controller is
synthesized by locally solving a semidefinite program offline for each
subsystem in a decentralized fashion. This program comprises local conditions
ensuring that the corresponding subsystem is locally passive. Passivity is
ensured with respect to a local virtual output which is different from the
local actual output. The program also comprises local conditions ensuring that
the local passivity of all subsystems implies the asymptotic stability of the
whole system. The performance of the proposed controller is evaluated on a case
study in DC microgrids.
