  Although transmission of a data packet containing sensory information in a
networked control system improves the quality of regulation, it has indeed a
price from the communication perspective. It is, therefore, rational that such
a data packet be transmitted only if it is valuable in the sense of a
cost-benefit analysis. Yet, the fact is that little is known so far about this
valuation of information and its connection with traditional event-triggered
communication. In the present article, we study this intrinsic property of
networked control systems by formulating a rate-regulation tradeoff between the
packet rate and the regulation cost with an event trigger and a controller as
two distributed decision makers, and show that the valuation of information is
conceivable and quantifiable grounded on this tradeoff. In particular, we
characterize an equilibrium in the rate-regulation tradeoff, and quantify the
value of information $\text{VoI}_k$ there as the variation in a so-called value
function with respect to a piece of sensory information that can be
communicated to the controller at each time $k$. We prove that, for a
multi-dimensional Gauss-Markov process, $\text{VoI}_k$ is a symmetric function
of the discrepancy between the state estimates at the event trigger and the
controller, and that a data packet containing sensory information at time $k$
should be transmitted to the controller only if $\text{VoI}_k$ is nonnegative.
Moreover, we discuss that $\text{VoI}_k$ can be computed with arbitrary
accuracy, and that it can be approximated by a closed-form quadratic function
with a performance guarantee.
