  Transmit power control is one of the most important issues in wireless
networks, where nodes typically operate on limited battery power. Reducing
communicating power consumption is essential for both economic and ecologic
reasons. In fact, transmitting at unnecessarily high power not only reduces
node lifetime, but also introduces excessive interference and electromagnetic
pollution. Existing work in the wireless community mostly focus on designing
transmit power policies by taking into account communication aspects like
quality of service or network capacity. Wireless networked control systems
(WNCSs), on the other hand, have different and specific needs such as
stability, which require transmit power policies adapted to the control
context. Transmit power design in the control community has recently attracted
much attention, and available works mostly consider linear systems or specific
classes of non-linear systems with a single-link view of the system. In this
paper, we propose a framework for the design of stabilising transmit power
levels that applies to much larger classes of non-linear plants, controllers,
and multi-link setting. By exploiting the fact that channel success
probabilities are related to transmit power in a non-linear fashion, we first
derive closed-loop stability conditions that relate channel probabilities with
transmission rate. Next, we combine these results together with well-known and
realistic interference models to provide a design methodology for stabilising
transmit power in non-linear and multi-link WNCSs.
