Two-Objective Filtering for Takagi–Sugeno Fuzzy Hopfield Neural Networks with Time-Variant Delay

This paper focuses on the issue of two-objec-tive filtering for Takagi–Sugeno fuzzy Hopfield neural networks with time-variant delay. The intention is to design a fuzzy filter subject to random occurring gain perturbations to make sure that the filtering-error system achieves a pre-defined $${\mathscr {H}}_{\infty }$$ and $${\mathscr {L}}_{2}\mathscr {-L}_{\infty }$$ disturbance attenuation level in mean square simultaneously. Without imposing any additional constraints on the differentiability of the time-delay function, a criterion of the mean-square $${\mathscr {H}}_{\infty }$$ and $${\mathscr {L}}_{2}\mathscr {-L} _{\infty }$$ performance analysis for the filtering-error system is derived by means of an augmented Lyapunov functional and the second-order Bessel–Legendre inequality. Then, a numerically tractable design scheme is developed for the desired non-fragile $${\mathscr {H}}_{\infty }$$ and $$ {\mathscr {L}}_{2}\mathscr {-L}_{\infty }$$ filter, where the gains are able to be determined by the solution of some linear matrix inequalities. At last, a numerical example with simulations is provided to illustrate the applicability and superiority of the present $${\mathscr {H}}_{\infty }$$ and $$ {\mathscr {L}}_{2}\mathscr {-L}_{\infty }$$ filtering method.