On zeno behavior in event-triggered control of networked systems

In networked systems, Zeno behavior denotes the phenomenon in which an infinite number of transmissions occur in a finite time interval. This phenomenon is extremely undesirable in event-triggered control, which aims at saving communication resources by relating the transmission scheduling with online information. This chapter studies the existence of Zeno behavior in event-triggered control with error-based triggering conditions. It is shown that Zeno behavior is closely related to some particular states, which make the threshold functions in triggering conditions equal to zero. Three kinds of event-triggered control systems, namely, the systems with relative triggering conditions, the finite-time event-triggered control systems, and the systems with external threshold signals, are investigated in detail. The corresponding necessary or sufficient conditions for Zeno behavior are obtained. Based on these analyses, it is discovered that an event-triggered control system with a linear plant can be internally stable but not input-to-state stable with respect to external disturbances; some conflicts between finite-time stability and event-triggered control are pointed out; and the difference between the concepts of Zeno-freeness and an event-separation property is revealed. Several numerical examples and simulations are provided to illustrate the feasibility of the proposed results.