9. Discrete-Time Networked Control Under Scheduling Protocols

This chapter analyzes the exponential stability of discrete-time networked control systems via delay-dependent Lyapunov-Krasovskii methods. The time-delay approach has been developed recently for the stabilization of continuous-time networked control systems under a Round-Robin protocol and a weighted Try-Once-Discard protocol, respectively. In the present chapter, the time-delay approach is extended to the stability analysis of discrete-time networked control systems under both these scheduling protocols. First, the closed-loop system is modeled as a discrete-time switched system with multiple and ordered time-varying delays under the Round-Robin protocol. Then, a discrete-time hybrid system model for the closed-loop system is presented under these protocols. It contains time-varying delays in the continuous dynamics and in the reset conditions. The communication delays are allowed to be larger than the sampling intervals. Polytopic uncertainties in the system model can be easily included in our analysis. The efficiency of the time-delay approach is illustrated in an example of a cart-pendulum system.