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The paper presents the theoretical analysis and simulation verification of robust fault diagnosis and adaptive parameter identification for single phase transformerless inverters. The fault diagnosis is composed of two parts, fault detection and fault identification. In the fault detection part, a Luenberger observer is designed to realize the detection of faults. Then, we apply a bank of observers to identify the location of faults. Meanwhile, the fault identification observers based estimation along with a gradient descent algorithm are also used in the parameter identification to estimate the actual values of components in a single phase transformerless inverter. Not only we develop the design methodology for the robust fault diagnosis and adaptive parameter identifier but also we present simulation results. The simulation results show the effectiveness of fault diagnosis and the accurate tracking of changes in component parameters for a wide range. [ABSTRACT FROM AUTHOR]