Networked Control with a Stochastic Scheduling: A Time-Delay Approach

This paper is concerned with the stability analysis of networked control systems with communication constraints, variable delays and variable sampling intervals. The scheduling of sensor communication is defined by a stochastic protocol. The activation probability of each sensor node is a given constant, whereas it is assumed that collisions occur with a certain probability. The resulting closed-loop system is a stochastic impulsive system with delays in the continuous dynamics and in the reset equations. The system matrices have stochastic parameters with Bernoulli distributions. Sufficient conditions for the exponential mean-square stability are derived via a Lyapunov-Krasovskii-based method. The efficiency of the method is illustrated on the example of a batch reactor. It is demonstrated how our time-delay approach allows treating network-induced delays larger than the sampling intervals.