Fault estimation using adaptive observer-based technique for time delay fractional-order systems

This paper proposes a technique to detect and estimate faults for fractional-order systems with time delay. Two observers are used in this method. Indeed, a time-delay fractional Luenberger observer is generated to detect fault. An adaptive fractional order with time delay observer is then constructed to estimate the fault by providing an on-line estimation algorithm. The convergence criteria of this observer is expressed via linear matrix inequalities (LMIs) by the use of a specific Lyapunov function considering the continuous frequency disturbed model. The validity of the fault detection and estimation technique is shown by a numerical example.