On quantized control for Markovian jump linear system over networks with limited information

In this paper, we deal with the problem of quantized control strategy design for a class of discrete time Markovian jump linear systems with limited communication capacity. We generalize the static Quantizer design method of Elia and Mitter to stochastic system with Markovian jump parameter. The concept of mode-dependent logarithmic quantizer is presented firstly in this paper, which is employed to ensure the stochastic stability of the quantized closed-loop system. For the logarithmic mode-dependent quantizer, it is shown that for each mode the corresponding individual quantizer possess the logarithmic characterization. Moreover, by including the transition rates of mode, the proposed mode-dependent quantizer can overcome the effect of Markovian switching. A numerical example is exploited to show the usefulness of the results derived.