Finite-Time Observability of Boolean Networks With Markov Jump Parameters Under Mode-Dependent Pinning Control

Finite-time observability of switching Boolean networks (SBNs) with Markov jump parameters (MJPs) is studied in this article. Via a parallel extension method, the observability of the considered SBN with MJPs is equivalent to that zero vector is reachable from an initial set of the new constructed system. A necessary and sufficient condition based on the extended structure matrix is presented for finite-time observability. Further, for unobservable systems, mode-dependent pinning control is first introduced and applied to achieve the observability. After the set of pinning subsystems is selected, for each pinning subsystem, mode-dependent pinning nodes, output-feedback controls (OFCs), and the adding approaches are designed. An algorithm is provided to find the set of pinning subsystems. Moreover, a necessary condition is given to solve mode-dependent pinning nodes, and the solvability of mode-dependent OFCs and the adding approaches are guaranteed. Finally, a numerical example is presented to show the effectiveness of the obtained results.