Inter-Event Time Analysis in Probability for Stochastic Linear Event-Triggered Control Systems

In this study, the properties of inter-event times in probability for stochastic linear event-triggered control systems are explored. The analysis of inter-event intervals is conducted for three distinct classes of event-triggering mechanisms: the absolute, relative, and mixed ones. Given the inherent stochastic nature of systems, it is challenging to achieve a certain judgment on avoiding Zeno behavior, where events occur at an infinite frequency. To address this issue, a probabilistic approach to examine the inter-event times is employed. It enables us to quantify the likelihood of Zeno behavior occurring in different scenarios, providing valuable insights into the performance of stochastic event-triggered control systems. Our research reveals substantial differences in the likelihood on the occurrence of a positive minimum inter-event interval among different mechanisms. Specifically, the mixed event-triggering mechanism emerges as the most probable one to yield a positive minimum inter-event time, indicating its potential superiority in efficiency. Conversely, some solutions of relative event-triggered control are proved to exhibit Zeno behavior with a probability of 1. Finally, a numerical example is provided to illustrate the efficiency and feasibility of the obtained results.