Abstract
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.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China Nos. (61806004 and 61503002), the Open Project of AnHui Province Key Laboratory of Special and Heavy Load Robot under Grant TZJQR005-2020, and the Excellent Youth Talent Support Program of Universities in Anhui Province (GXYQZD2019021).
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Hu, Q., Chen, L., Zhou, J. et al. Two-Objective Filtering for Takagi–Sugeno Fuzzy Hopfield Neural Networks with Time-Variant Delay. Neural Process Lett 53, 4047–4071 (2021). https://doi.org/10.1007/s11063-021-10580-0
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DOI: https://doi.org/10.1007/s11063-021-10580-0