Minimum-Time and Minimum-Triggering Observability of Stochastic Boolean Networks
Shiyong Zhu, Jianquan Lu, Lin Lin, Yang Liu
Abstract
This article investigates the observability of Markovian jump Boolean networks (MJBNs) via algebraic state space representation approach. A necessary and sufficient criterion in the form of linear programming is derived for the asymptotic observability in distribution of MJBNs, and several conditions are obtained for the finite-time observability based on the properties of nilpotent matrices. Subsequently, in order to minimize the time consumption, a maximum principle is established to address the minimum-time observability problem. With regard to the event-triggered output feedback observability, an efficient procedure is developed to minimize the number of triggering events. Finally, three numerical examples are employed to demonstrate the effectiveness of theoretical results.