Bit Rate Conditions to Stabilize Quantized Markov Jump Linear Systems

This paper investigates the mean square stability (MSS) of quantized Markov jump linear systems (MJLSs) based on networked control, where the control loop is formed in a digital feedback path. Taking channel capacity constraints into account, we mainly research on the effects of finite constant bits quantization on the MJLSs’ stability. The original system is stabilized by pre-processing coordination transformation of the system matrices and constructing a corresponding strategy of quantization and control. Sufficient and necessary bit rate conditions required to mean square stabilize the system are finally obtained, while these two conditions define the range that the minimum bit rate is located in. The gap between the conditions is narrowed by the method proposed by this paper compared to existed results. We also extend the bit rate conditions to the case that system state cannot be directly accessed through constructing a mode-dependent state observer. Numerical example is used to verify the achieved theoretical results.