Bisimulations for delayed switched Boolean control networks and its application in controllability

Abstract

Abstract This paper investigates bisimulation relations of delayed switched Boolean control networks (DSBCNs), using the semi‐tensor product (STP) approach. Firstly, the notion of bisimulation in DSBCNs is formalized. Subsequently, based on the skeleton matrix of DSBCN, two necessary and sufficient conditions are derived for checking this notion. Moreover, as an application of bisimulation relations, this paper explores the propagation of controllability for DSBCNs through a bisimulation relation. It shows the possibility that the controllability of a DSBCN can be inferred by studying a potentially simpler DSBCN. At last, two examples are proposed to illustrate the efficiency of the obtained results.

Keywords

• Bisimulations
• controllability
• delayed switched Boolean control networks
• semi‐tensor product