  We discuss the scheduling of a set of networked control systems implemented
over a shared communication network. Each control loop is described by a
linear-time-invariant (LTI) system with an event-triggered implementation. We
assume the network can be used by at most one control loop at any time instant
and after each controller update, a pre-defined channel occupancy time elapses
before the network is available. In our framework we offer the scheduler two
options to avoid conflicts: using the event-triggering mechanism, where the
scheduler can choose the triggering coefficient; or forcing controller updates
at an earlier pre-defined time. Our objective is avoiding communication
conflict while guaranteeing stability of all control loops. We formulate the
original scheduling problem as a control synthesis problem over a network of
timed game automata (NTGA) with a safety objective. The NTGA is obtained by
taking the parallel composition of the timed game automata (TGA) associated
with the network and with all control loops. The construction of TGA associated
with control loops leverages recent results on the abstraction of timing models
of event-triggered LTI systems. In our problem, the safety objective is to
avoid that update requests from a control loop happen while the network is in
use by another task. We showcase the results in some examples.
