On Controllability and Stabilization of Switched Logical Control Networks With Switching-Input-Triggered Restricted Successors

This article presents a systematic investigation for the controllability and stabilization of switched logical control networks (SLCNs) with switching-input-triggered restricted successors (SIT-RS). In this context, the switching and input signals are constrained by their combinations at the previous step. Using the semi-tensor product tool, SIT-RS are reinterpreted as unilateral restricted successors for a combined variable. Under this framework, augmented Markovian auxiliary system and augmented linear auxiliary system are, respectively, constructed, serving as pivotal bridges to derive the sufficient and necessary criteria for finite-time weak (respectively, strong) controllability of SLCNs with SIT-RS. Furthermore, the above criteria are optimized when considering the cases without isolated pairs. Besides, a reduced Markovian auxiliary system (RMAS) is established via deleting isolated pairs iteratively. By analyzing the admissible maximum simple paths on digraph generated from RMAS and the single-switching-input-based fixed point, a sufficient and necessary criterion, as well as an algorithm for point stabilization of SLCNs with SIT-RS is derived. Finally, two biological examples are given to verify the obtained results.