This paper investigates networked control of a collection of battery-powered systems with seriously limited communication capacity and power resources. We aim to stabilize the systems by effectively assigning the communication channels and appropriately allocating the transmission powers so that the energy consumption is within an energy budget. The role of channel assignment is to guarantee network access for all plants when needed; the mission of power allocation is to ensure a desired rate of successful packet transmission for each channel. These two aspects are achieved by a scheduling policy and a power allocation method, respectively, each of which is derived based on stability and schedulability requirements. An interesting co-design framework is derived for communication scheduling, transmission power allocation and stabilizing control. The presented methodology can guarantee a desired decay rate and a given energy consumption for each plant. The effectiveness of the results is demonstrated by numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd.