Networked Control Under Round-Robin Protocol

Abstract

In Chaps. 2 and 3, we have considered the case of one sensor node. In this chapter, we propose a time-delay approach to the stability and $L_2$-gain analysis of NCSs with multiple sensor nodes. For the sake of simplicity, we consider only two sensor nodes. Due to communication constraints, the scheduling of sensor information toward the controller is ruled by the classical Round-Robin protocol. The closed-loop system is modeled as a switched continuous-time system with multiple and ordered time-varying delays. The case of the ordered time-varying delays (where one delay is smaller than another) has not been studied yet in the literature. By developing appropriate Lyapunov–Krasovskii techniques in this case, we derive LMIs for the exponential stability and for the $L_2$-gain analysis. The efficiency and advantages of the proposed approach are illustrated by two benchmark examples. The numerical results essentially improve the hybrid system-based existing ones [84] and, for the stability analysis, are not far from those obtained via the discrete-time approach [29]. Note that the latter approach is not applicable to the performance analysis. Also, for the first time (under Round-Robin scheduling protocol), the network-induced delay is allowed to be greater than the sampling interval.