Transmit power control is crucial in wireless networks due to limited battery power, impacting both economic and environmental aspects by reducing power consumption. High transmission power diminishes node lifespan, causes interference, and pollution. Existing work in wireless networks mainly focuses on power policies for communication aspects like quality of service and channel capacity, while wireless networked control systems (WNCSs) require adapted policies for control-oriented requirements such as stability. Recent research in the control community has predominantly focused on linear systems or non-linear systems with a single-link perspective. This paper introduces a framework for designing stabilising transmit power levels for broader classes of non-linear plants and multi-link scenarios. By considering the non-linear relationship between channel success probabilities and transmit power, we establish stability conditions linking channel probabilities and transmission rate. These results, along with practical interference models, offer a methodology for stabilising transmit power in non-linear and multi-link WNCSs.