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

• Published in: Neural processing letters 2021-12, Vol.53 (6), p.4047-4071
• Main Authors: Hu, Qi, Chen, Lezhu, Zhou, Jianping, Wang, Zhen
• Format: Article
• Language: English
• Subjects: Artificial Intelligence; Artificial neural networks; Complex Systems; Computational Intelligence; Computer Science; Delay; Design techniques; Error analysis; Euclidean space; Filtration; Fuzzy logic; Fuzzy sets; H infinity; Inequality; Linear matrix inequalities; Mathematical analysis; Neural networks; Random variables
• ISSN: 1370-4621; 1573-773X
• DOI: 10.1007/s11063-021-10580-0

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 H ∞ and L 2 - L ∞ 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 H ∞ and L 2 - L ∞ 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 H ∞ and L 2 - L ∞ 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 H ∞ and L 2 - L ∞ filtering method.