Self-triggered control for approximate synchronization of singular logical networks

This paper investigates the approximate synchronization of singular logical networks (SLNs) using algebraic representations. Different from complete synchronization, which requires the state trajectories of the drive-response SLNs to be completely consistent after a finite time, approximate synchronization allows for admissible errors between the state trajectories of the drive-response SLNs. A definition of approximate synchronization for SLNs is proposed. By analyzing the constructed admissible matrices, the solvability of SLNs is discussed. A criterion is provided for the approximate synchronization of SLNs. Self-triggered control is then introduced to address the approximate synchronization of SLNs. Based on this, an algorithm is presented for designing the self-triggered state feedback control of approximate synchronization. The method presented in this paper can significantly reduce the updating frequencies of the controller. Finally, all the theoretical results are illustrated through a genetic regulatory network.