Fault diagnosis and prognosis in discrete event systems are studied in the scenario where the observations are possibly received with delay. To address this scenario, two conditions for diagnosis and prognosis with delayed observations are proposed, where we show that the state-of-the-art notion of prognosability must be revised to avoid conservativeness. Diagnosability and prognosability conditions are then verified by introducing a delay observer and a new verification function. Theoretical analysis indicates the effectiveness of the verification method for fault diagnosis and prognosis in the system.
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