Robust Fault Estimation for Takagi–Sugeno Nonlinear Systems with Time-Varying State Delay

This paper addresses the problem of robust fault estimation for Takagi–Sugeno (T–S) nonlinear systems with time-varying state delay. Under $$H_{\infty }$$H∞ performance constraint, a fuzzy-augmented fault estimation observer (AFEO) design is proposed to enhance the performance of fault estimation for T–S nonlinear state delay models with actuator and sensor faults simultaneously. Based on Lyapunov function and improved free-weighting approach, some less conservative sufficient conditions for the existence of AFEO are given in terms of linear matrix inequalities, and the obtained fault estimates via AFEO can practically better depict the size and shape of the faults. Finally, three illustrative examples are given to illustrate the validity of the proposed design procedures.