  In this paper, we study the trade-off between the transmission cost and the
control performance of the multi-loop networked control system subject to
network-induced delay. Within the linear-quadratic-Gaussian (LQG) framework,
the joint design of control policy and networking strategy is decomposed into
separation optimization problems. Based on the trade-off analysis, a scalable,
delay-dependent Value-of-Information (VoI) based scheduling policy is
constructed to quantify the value of transmitting the data packet, and enables
the decision-makers embedded in subsystems to determine the transmission
policy. The proposed scalable VoI inherits the task criticality of the previous
VoI metric meanwhile is sensitive to the system parameters such as information
freshness and network delays. The VoI-based scheduling policy is proved to
outperform the periodical triggering policy and existing Age-of-Information
(AoI) based policy for network control system under transmission delay. The
effectiveness of the constructed VoI with arbitrary network delay is validated
through numerical simulations.
