We consider a system controlled by a human operator. The system is modeled by a Petri net and its normal state is specified by a linear inequality on the set of reachable markings. Admissible behaviors of the operator are given by an invariance based control technique. We extend a failure diagnosis method proposed by Sampath et al. to the case that the system has self-recovery. We introduce a novel concept called weak diagnosability. We propose an error detector and show a condition for the system to be weakly diagnosable.