Multi-objective optimization-based robust fault estimation observer design for fuzzy singularly perturbed systems with time-varying state delays

In this paper, the problem of multi-objective robust fault estimation based on observer is addressed for T-S fuzzy nonlinear singularly perturbed systems with time-varying state delay and external disturbance. Under H infinity$$ {H}_{\infty } $$ performance constraint, a fuzzy augmented fault estimation observer is introduced to improve the performance of actuator and sensor fault estimation simultaneously. The sufficient conditions for the existence of fault estimator are given in the form of LMIs, where epsilon$$ \varepsilon $$-dependent Lyapunov function is considered. The given multi-objective fault estimator design strategy has a good ability to suppress external disturbance and ensure the estimation accuracy and convergence rate work well for all epsilon is an element of(0,epsilon?]$$ \varepsilon \in \left(0,\overline{\varepsilon}\right] $$. Then the largest stability bound and the best attenuation capacity are guaranteed by deriving a modified optimal algorithm. Finally, two examples are given to illustrate the feasibility and correctness of the proposed design method.