Networked control of stochastic systems with scheduling protocols

In the present paper, we extend the time-delay approach to networked stochastic systems with state multiplicative noise. Two classes of protocols are considered. The first one is defined by Round-Robin (RR) protocol where the sampled measurements are sent in a periodic manner one after another, whereas the second is defined by try-once-discard (TOD) protocol where the sampled measurements sent have the greatest weighted error. The resulting closed-loop systems are modeled as a system with multiple time-varying delays and a hybrid system with a time-varying delay in the dynamics and in the reset conditions, respectively. By use of Lyapunov-Krasovskii approach, sufficient conditions for guaranteeing the exponential mean square stability are obtained in terms of linear matrix inequalities (LMIs). An example of batch reactor illustrates the efficiency of the results.