## 1 Introduction  
With recent advances in wireless technologies, wireless control systems (WCSs) are attracting increasing attention from both academia and industry [1-4]. In a WCS, spatially distributed nodes of sensors, controllers and/or actuators are interconnected with wireless links. The use of wireless technologies in control applications has many advantages compared to wired networked control systems that are dominant at the moment. For instance, wireless networks allow flexible installation and maintenance, mobile operation, and monitoring and control of equipments in hazardous and difficult-to-access environments. Another important factor that instigates the deployment of wireless sensor/actuator networks is their relatively cheaper costs. However, wireless communications raise new challenges for control system analysis and design. Wireless channels have adverse properties, such as path loss, multi-path fading, adjacent channel interference, Doppler shifts, and half-duplex operations [1]. While traditional wired networks usually have fixed communication capacity, the link capacity of wireless channels may vary significantly over time [5-7]. Because the operations of wireless transceivers are half-duplex, wireless systems cannot support non-destructive medium access control (MAC) protocols. From the control point of view, communication networks introduce problems related to delay, packet losses, and jitters. Compared with wireless, wireless links make these problems more pronounced [8,9]. For instance, the bit error rate of a wireless channel is typically several times higher than that of a wired connection [10]. These phenomena degrade the quality of control (QoC), or even cause system instability in extreme circumstances [5,11]. The area of WCSs is still in its infancy. The suitability of diverse wireless technologies for control applications has been studied through both simulations [12-14] and experiments [7,10,15]. A number of proposals on modifying established communication mechanisms for wireless networks to achieve real-time guarantees have been presented, e.g. [16,17]. Some other researchers, mostly from the control community, attempt to design controllers robust to the temporal non-determinism of wireless networks, for example, [6,18]. In contrast to all these papers, the focus of this work is on co-design of real-time control and wireless communications. Because of its interdisciplinary nature, this co-design is complicated, with limited results reported in the literature. [PERSON] and [PERSON] [19] introduced the methodology of cross-layer design into WCS design, and presented a four-layer framework. But adaptation of the sampling periods of control loops is not considered. Through studying the impact of varying fading wireless channels on control performance, [PERSON] and [PERSON] [5] suggested that the controller parameters should be dynamically adapted with respect to channel conditions. An offline approach to optimize the stationary performance of a linear control system by jointly allocating communication resources and tuning parameters of the controller is presented in [20]. Different methods for adapting sampling periods at runtime have been developed in e.g. [10,11,21]. All these methods are based on algorithms with fixed parameters. Consequently, the effects of varying channel conditions such as changes in network transmission rates are not attacked. In our recent work [3,4,9], we presented several design methods for control systems over wireless networks. An integrated framework that adjusts the maximum number of allowable data retransmission attempts and tunes the controller parameters is given in [22]. Different approaches to dynamic bandwidth allocation through dynamically adjustingsampling periods are presented in [23, 24] for wireline networked control systems. Additionally, almost all existing solutions for online sampling period adjustment are time triggered.