State Feedback Stabilization Over Finite-State Fading Channels

This paper studies state feedback stabilization over finite-state fading channels, where the stochastic characteristic of time-varying fading channels is assumed to be driven by a finite-state random process. The finite-state process is used to represent different channel fading amplitudes and/or to model different configurations of the overall physical environment. A series of necessary and sufficient conditions are given for stabilization over finite-state Markov fading channels. In the case of finite-state independent and identially distributed fading channels, explicit network requirements for stabilization are presented for both single-input case and multi-input case. It is shown that our results cover some existing results as special cases. Finally, the results are applied to stabilization of a single-input plant over a Gilbert-Elliott channel demonstrated by numerical simulations.