Minimal observability of periodically switching Boolean networks

This paper primarily delves into the minimal observability problem of periodically switching Boolean networks (PSBNs) using semi-tensor product (STP) of matrices. Firstly, a method for calculating all indistinguishable states is obtained based on the algebraic form of the periodically switching Boolean network (PSBN). Secondly, a specific step to calculate the states that need to become initially distinguishable in the indistinguishable state set is given by establishing a parallel system and applying the set reachable method. Subsequently, the minimal observability of the system is achieved by adding the minimum number of measurements to the system. Finally, the validity of the conclusion is verified through some illustrative examples.