Event-triggered set stabilization of impulsive logical control networks based on the hybrid index model approach

Abstract

This paper proposes two kinds of event-triggered control (ETC) schemes to stabilize k-valued impulsive logical control networks (ILCNs) towards a given state set. It is worth pointing out that the impulsive process of traditional ILCNs is usually assumed to occur in a unit of time, which neglects continuous impulsive jumpings. In contrast, ILCNs here are redefined based on a 2-D index model to demonstrate the detailed impulsive process. In this ground, we establish the set stabilization criteria for ILCNs in both the hybrid domain and the time domain. It reveals that if an ILCN achieves set stabilization in the hybrid domain, it must achieve set stabilization in the time domain, but not vice versa. Then, two types of ETC, which obey the event-triggered inputting strategy and event-triggered updating strategy, are designed in the hybrid domain and the time domain. Finally, a biological example is presented to elaborate on the controller design procedures.