Feedback Stabilization of Discrete-Time Networked Systems Over Fading Channels

This paper addresses the mean square stabilization problem for discrete-time networked control systems over fading channels. We show that there exists a requirement on the network over which an unstable plant can be stabilized. In the case of state feedback, necessary and sufficient conditions on the network for mean square stabilizability are derived. Under a parallel transmission strategy and the assumption that the overall mean square capacity of the network is fixed and can be assigned among parallel input channels, a tight lower bound on the overall mean square capacity for mean square stabilizability is presented in terms of the Mahler measure of the plant. The minimal overall capacity for stabilizability is also provided under a serial transmission strategy. For the case of dynamic output feedback, a tight lower bound on the capacity requirement for stabilization of SISO plants is given in terms of the anti-stable poles, nonminimum phase zeros and relative degree of the plant. Sufficient and necessary conditions are further derived for triangularly decoupled MIMO plants. The effect of pre- and post-channel processing and channel feedback is also discussed, where the channel feedback is identified as a key component in eliminating the limitation on stabilization induced by the nonminimum phase zeros and high relative degree of the plant. Finally, the extension to the case with output fading channels and the application of the results to vehicle platooning are presented.