Takagi–Sugeno Fuzzy Hopfield Neural Networks for $${\mathcal{H}_{\infty}}$$ Nonlinear System Identification

In this paper, we propose a new $${\mathcal H_\infty}$$ weight learning algorithm (HWLA) for nonlinear system identification via Takagi–Sugeno (T–S) fuzzy Hopfield neural networks with time-delay. Based on Lyapunov stability theory, for the first time, the HWLA for nonlinear system identification is presented to reduce the effect of disturbance to an $${\mathcal{H}_{\infty }}$$ norm constraint. The HWLA can be obtained by solving a convex optimization problem which is represented in terms of linear matrix inequality (LMI). An illustrative example is given to demonstrate the effectiveness of the proposed identification scheme.

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