In the context of fault detection and isolation of linear parameter-varying systems, a challenging task appears

when the dynamics and the available measurements render the model unobservable, which invalidates the

use of standard set-valued observers. Two results are obtained in this paper, namely, using a left-coprime

factorization, one can achieve set-valued estimates with ultimately bounded hyper-volume and convergence

dependent on the slowest unobservable mode; and by rewriting the set-valued observer equations and taking

advantage of a coprime factorization, it is possible to have a low-complexity fault detection and isolation

method. Performance is assessed through simulation, illustrating, in particular, the detection time for various

types of faults.