Discrete-time networked control systems under stochastic scheduling constraints

Abstract

This paper extends the time-delay approach to discrete-time networked control systems with multiple sensor nodes that are subject to time-varying transmission intervals, time-varying transmission delays and communication constraints. The system sensor nodes are supposed to be distributed over a network. The scheduling of sensor communication is ruled by an independent and identically-distributed stochastic process. The activation probability of each sensor node is a given constant, whereas it is assumed that collisions occur with a certain probability. The closed-loop system is modelled as a discrete-time stochastic hybrid system with time-varying delays in the dynamics and in the reset conditions. By Lyapunov method a new condition is derived for the exponential mean-square stability of the delayed hybrid systems with respect to the full state and not only to the partial state. The communication delays are allowed to be greater than the sampling intervals. The efficiency of the proposed method is illustrated on the example of cart-pendulum.