Improved stability conditions for discrete-time systems under dynamic network protocols

This paper deals with the stability of discrete-time networked systems with multiple sensor nodes under dynamic scheduling protocols. Access to the communication medium is orchestrated by a weighted try-once-discard or by an independent and identically-distributed stochastic protocol that determines which sensor node can access the network at each sampling instant and transmit its corresponding data. Through a time-delay approach, a unified discrete-time hybrid system with time-varying delays in the dynamics and in the reset conditions is formulated under both scheduling protocols. Then, a new stability criterion for discrete-time systems with time-varying delays is proposed by the discrete counterpart of the second-order Bessel-Legendre integral inequality. The developed approach is applied to guarantee the stability of the resulting discrete-time hybrid system model with respect to the full state under try-once-discard or independent and identically-distributed scheduling protocol. The communication delays can be larger than the sampling intervals. Finally, the efficiency of the presented approach is illustrated by a cart-pendulum system.