Asynchronous Quantization Control of Stochastic Markov Jump Systems with Round-Robin Protocol

This paper investigates the asynchronous quantized control problem for stochastic Markov jump systems (SMJSs). A round-robin protocol is employed in the sensor-controller network to efficiently manage the transmission of measurement data from multiple sensor nodes. The measurement outputs are quantized using a logarithmic quantizer. A hidden Markov model characterizes the asynchrony between the plant and controller modes. By applying the delay transformation method and the equal-period sampling strategy, the SMJS under the round-robin protocol is transformed into the SMJS with time delay. A Lyapunov-Krasovskii functional is then constructed, and stochastic analysis techniques are utilized to derive a criterion for mean-square exponential stability. Finally, the effectiveness of the proposed method is demonstrated through a numerical simulation.