Distributed event-triggered fault estimation for Takagi–Sugeno multi-agent systems with unmeasurable decision variables

This paper proposes a novel distributed fault estimation framework for a class of nonlinear multi-agent systems (MASs), addressing time-varying multiplicative and additive faults in both actuators and sensors. To address these challenges, the Takagi–Sugeno (T-S) system model is employed, incorporating unmeasurable decision variables, which introduces more complexity compared to known decision variables. This study pioneers the one-sided Lipschitz approach in this context, offering significant advancements over the traditional Lipschitz method. A two-step design process is presented to estimate system states, faults, and external disturbances through an $\ell$th-order proportional-integral observer and a constrained least squares estimator, which is data-driven. Agents can update their observers by using relative residual outputs derived from neighboring information, enhancing both fault and state estimation accuracy. Furthermore, a dynamic event-triggered communication protocol enables efficient output sharing and reduces communication costs. The observer design conditions are formulated as an optimization problem constrained by linear matrix inequalities, ensuring robust H-infinity performance. Simulation results validate the effectiveness of the proposed method for robust fault estimation in nonlinear MASs.