Stabilization of Markovian Jump Boolean Control Networks via Event-Triggered Control

Abstract

In this article, we investigate the stabilization of Markovian jump Boolean control networks by a kind of event-triggered control, which is essentially an intermittent control scheme. First, a novel condition for the stability of Markovian jump Boolean networks is obtained based on the recurrence of finite-state homogeneous Markov chains. After that, the necessary and sufficient conditions for the stabilization of a Markovian jump Boolean control network by an event-triggered control are proposed based on an associated digraph, and the design method of the corresponding event-triggered control is given. Furthermore, in order to save control costs, we construct an event-triggered control with a minimal event-triggering set for the stabilization of the Markovian jump Boolean control network by finding a minimum-weight spanning branching forest of the associated digraph. Finally, an example is given to illustrate the effectiveness of the obtained results.