An event-based state estimation approach for positive systems with positive observers

This article addresses the problem of state observer design and robustness with respect to uncertain dynamics for continuous-time linear positive networked systems. Considering the bandwidth constraint in the communication network, an event-measurement-based positive observer design is proposed. The physical interpretation of a positive observer differs from that of a general observer. Its primary goal is to ensure that all state estimates remain non-negative at all times. Using output measurements, a law with weighted sampling error is used to determine the sampling sequence between the system and the observer. The observer dynamics are designed using the standard Luenberger structure with the event-based sampled output information, which is updated only when an event occurs. Assuming observability and sufficient conditions for the positivity of the system, the asymptotic stability of the observer dynamics with sampled information is established. Sufficient conditions of stability and positivity are derived using linear matrix inequalities. Moreover, the design ensures that the event-based architecture is free from Zeno behavior, ensuring a positive minimum bound on the inter-execution time. The proposed positive observer is also shown to be robust to time-varying uncertainties, ensuring positivity, stability, and strictly positive inter-event times. In addition, numerical simulations on a three-tank system having variable cross-sections are used to demonstrate the efficacy of the proposed event-based positive observer.