Necessary and Sufficient Conditions for Event-Triggered Set Stabilizability of Markovian Jump Logical Networks
本文利用Lyapunov理论，为马尔可夫跳跃逻辑控制网络的事件触发集能稳定性建立了充要条件，并通过大肠杆菌乳糖操纵子生物实例验证了结果的有效性。
This technical paper utilizes the Lyapunov theory to characterize the event-triggered set stabilizability of Markovian jump logical control networks (MJLCNs). Whereas the existing result for checking the set stabilizability of MJLCNs is only sufficient, this technical paper further establishes its necessary and sufficient condition. First, the Lyapunov function is established to describe the set stabilizability of MJLCNs necessarily and sufficiently by combining recurrent switching modes and desired state set. Then, the triggering condition and the input updating mechanism are designed regarding the value change of the Lyapunov function. Finally, the effectiveness of theoretical results is demonstrated by a biological example concerning the lac operon in Escherichia coli.