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 [2] 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.