Sampled-Data Set Stabilization of Impulsive Boolean Networks Based on a Hybrid Index Model

Abstract

This article investigates the set stabilization of impulsive Boolean control networks (IBCNs) by sampled-data state feedback control based on a hybrid index model. It is worth mentioning that the 2-D index model has the ability to characterize the instantaneousness of ideal impulses and describe complicated impulsive behaviors. To avoid Zeno phenomenon, the judging conditions for forward completeness are derived. Subsequently, an algorithm is designed to obtain the largest sampled point control invariant set (SPCIS) of a given set in the hybrid domain, and its validity is further authenticated. Accordingly, a necessary and sufficient condition is derived for the set stabilization of IBCNs in the hybrid domain, and all time-optimal sampled-data state feedback controllers are designed. The similar results are also obtained for IBCNs in the time domain. Compared with set stabilization in the time domain, set stabilization in the hybrid domain not only focuses on the dynamics at each time instant but also concerns every jumping state. It results in that every SPCIS in the hybrid domain is a subset of a certain SPCIS in the time domain. Eventually, the $\lambda$ switch with impulsive disturbances is modeled as a reduced IBCN, which is presented to demonstrate the obtained results.