Stabilization of Logical Dynamic Networks via Event-Triggered Switching Signals and Its Application

Abstract

This paper studies the stabilization of logical dynamic networks (LDNs) via event-triggered switching signals. Compared with existing results, the designed switching signal does not need to be updated at each time step, and it will greatly reduce the waste of resources in the process of information transmission. At present, most of the proposed event-triggered mechanisms (ETMs) for LDNs are available for special systems and are also difficult to implement in practice. Our goal is to propose an ETM with generality and strong operability, under which the designed switching signals can be used to stabilize the addressed system. Considering that the Lyapunov method can be successfully applied to investigating the stability of different LDNs, here we propose the concept of switching Lyapunov function and try to establish the ETM based on the switching Lyapunov function. A necessary and sufficient condition is derived from the existence of the switching Lyapunov function for the stabilization of LDNs via event-triggered switching signals. In terms of the obtained switching Lyapunov functions, two algorithms are further developed to seek the time-optimal switching sequence and cost-optimal switching sequence. Moreover, the obtained results are applied to the stabilization of LDNs with logical switching as well as impulsive LDNs. An example is finally given to show the effectiveness of the theoretical results.