Networked control under round-robin protocol: Multiple sensors and non-small communication delays

The existing results on Networked Control Systems (NCSs) in the presence of variable sampling intervals, communication delays and scheduling protocols (in the frameworks of hybrid and discrete-time systems) are confined to small communication delays (that are smaller than the sampling intervals). Recently the time-delay approach was suggested to NCSs with N = 2 sensors under Round-Robin (RR) and Try-Once-Discard (TOD) protocols [1], [2], where communication delays were allowed to be non-small. The objective of this paper is to extend the time-delay approach to NCSs under RR protocol with a general number N ≥ 2 of sensor nodes. To derive simple conditions we suggest a novel hybrid system model for the closed-loop system with time-varying delays in the dynamics and in the reset conditions. A new Lyapunov-Krasovskii method is introduced for the exponential stability of the resulting delayed hybrid systems. For the case of two sensors, the resulting conditions are computationally simpler than the existing ones of [1]. The communication delays are allowed to be greater than the sampling intervals. Polytopic type uncertainties in the system model can be easily included in the analysis. The efficiency of the time-delay approach is illustrated on the example of uncertain cart-pendulum.