Positive Unknown Input Observer for Fault Detection of Positive Distributed Systems

We consider robust fault detection in distributed systems with first and second order agent models. In such systems, we show that a ubiquitous class of consensus protocols leads to collective dynamics that lie in a nonnegative invariant set. Based on this, we derive LMI conditions for residual generators to sense faults in the nonnegative invariant set. An illustrative example is provided to highlight our approach and to show that it can reduce the time interval between fault occurrence and fault detection.