Robust Fault Estimation Based on a Learning Observer for Linear Continuous-Time Systems with State Time-Varying Delay

This study addresses the problem of robust actuator fault estimation for a class of critical linear continuous-time systems subject to state time-varying delays, external disturbances, and actuator faults. A learning observer is proposed to achieve the challenging task of simultaneously estimating both the system states and actuator faults, irrespective of whether the faults are constant or time-varying. A key theoretical contribution is the derivation of a less conservative delay-dependent condition for the existence of the proposed learning observer, which is expressed in terms of linear matrix inequalities (LMIs). The H∞ performance index is employed to attenuate the effects of disturbances to a prescribed level. The efficacy of the proposed strategy is rigorously validated through three illustrative examples, including quantitative performance metrics and a comparative analysis with existing methods.