Quantized feedback stabilization of discrete-time linear system with Markovian jump packet losses

In this paper, we mainly focus on the problem of quantized feedback stabilization of a discrete-time linear system with Markovian jump packet losses. Based on the packet loss dependent Lyapunov functions, the coarsest quantizer is analyzed in detail to guarantee the mean square quadratic stabilization of the system. If the system adopts the logarithmic quantizer, the necessary and sufficient conditions, which make the system mean square quadratically stabilized by a linear state feedback controller, can be converted into an algebraic Riccati equation and then into an LMI. Then based on this LMI, we obtain the infimum quantization density of the logarithmic quantizer over all dependent Lyapunov functions. Finally, a numerical example is presented to illustrate the effectiveness of the results obtained in this paper.