This technical note concerns fault detection and diagnosis for discrete event systems modeled with partially observed Petri nets. The proposed method provides diagnosis decisions via the analysis of observation sequences that include some observable events and the partial measurement of the successive states visited by the system. To this end, the observation sequences are decomposed into elementary observation sequences, linear matrix inequalities are used to compute the firing sequences consistent with each elementary observation sequence and an algorithm of linear complexity with respect to the length of the observation sequences is proposed to provide on-line diagnosis decisions.