Structural Monostability of Activation-Inhibition Boolean Networks

Although any networked control system is specified by the combination of the network structure and the dynamics of the components, one often encounters a situation where the former is known but the latter is (almost) unknown. In such a case, we cannot apply any analysis and design method using the full information of the target system. So it is desirable to establish a framework of the structural analysis and design, that is, an analysis and design methodology based on the information only on the network structure. This paper addresses the structural stability, that is, the stability with unknown component dynamics, for a class of networked control systems. In particular, we consider here Boolean networks and present a series of (necessary and) sufficient conditions for structural stability.