Robust Actuator Fault Reconstruction for Takagi-Sugeno Fuzzy Systems with Time-varying Delays via a Synthesized Learning and Luenberger Observer

This paper addresses the problem of robust actuator fault reconstruction for Takagi-Sugeno (T-S) fuzzy systems subjects to actuator faults, unknown inputs and time-varying delays via a Fuzzy Synthesized Learning and Luenberger Observer (FSL²O). Through a coordinate transformation, the original T-S fuzzy system is decomposed into two subsystems: subsystem-1 effected by actuator faults and subsystem-2 effected by unknown inputs. In the presented FSL²O methodology, a Reduced-Order Fuzzy Learning Observer (ROFLO) is explored for the subsystem-1 to reconstruct actuator faults accurately while a Reduced-Order Fuzzy State (Luenberger) Observer (ROFSO) is designed for the subsystem-2 based on the H_∞ control technique such that it has strong robustness against the unknown inputs. The synthesized design of the ROFLO and the ROFSO is formulated in a unified manner in terms of Linear Matrix Inequalities (LMIs) that can be conveniently solved using LMI optimization technique. In addition, as a comparison, a full-order FLO is suggested for robust actuator fault reconstruction. Finally, a numerical example and simulation are provided to demonstrate the effectiveness of the proposed approaches.