Quantized H ∞ filtering for discrete-time systems over fading channels

Abstract

This paper addresses the problem of quantized $H_{\infty }$ filtering for multi-output discrete-time systems over independent identically distributed (i.i.d.) fading channels and Markov fading channels, respectively. The measurement outputs are quantized by a logarithmic quantizer, and then transmitted to the filter over fading channels. For the i.i.d. fading channels, the stochastic multiplicative noise form is used to model the unreliable communication environment. For the Markov fading channels, a set of Markov channel state processes is introduced to model time-varying fading channels, which characterizes various configurations of the physical communication environment and/or different channel fading amplitudes. The sufficient condition for stochastic stability with a prescribed $H_{\infty }$ performance is obtained by using a Lyapunov method and matrix decoupling technique. The corresponding filter design casts into a convex optimization problem. Finally, simulation results are provided to illustrate the effectiveness of our results.