The communication protocol IEEE 802.15.4 is becoming pervasive for low power and low data rate wireless sensor networks (WSNs) applications, including control and automation. Nevertheless, there is not yet any adequate study about control systems networked by this protocol. In this paper, the stability of IEEE 802.15.4 networked control systems (NCSs) is addressed. While in recent works fundamental results are developed for networks that are abstracted only in terms of packet loss and time delays, here the constraints imposed by the protocol to the feedback channel and the network energy consumption are explicitly considered. A general analysis for linear systems with parameter uncertainty and external bounded disturbances with control loops closed over IEEE 802.15.4 networks is proposed. To reduce the number of transmissions and thus save energy, a self-triggered control strategy is used. A sufficient stability condition is given as function of both the protocol and control parameters. A decentralized algorithm to adapt jointly the self-triggered control and the protocol parameters is proposed. It is concluded that stability is not always guaranteed unless protocol parameters are appropriately tuned, and that event-triggered control strategies may be difficult to use with the current version of IEEE 802.15.4.