H<sub>∞</sub> Performance State Estimation for Static Neural Networks With Time-Varying Delays via Two Improved Inequalities
Yufeng Tian, Zhanshan Wang
Abstract
This brief studies the problem of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance state estimation for static neural networks with time-varying delays. A generalized double-integral inequality and a parameter-dependent reciprocally convex inequality are proposed, respectively, which encompass some existing results as their special cases. Combining the two improved inequalities and zero equality with two independent parameters, a less conservative H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance state estimation criterion is derived. The estimator gain matrices and the optimal performance index are obtained in terms of linear matrix inequalities (LMIs). Compared with some existing works, the designed estimator gain matrices are independent of activation function, which eliminates the restriction that the activation function has to be invertible. A numerical example is illustrated to verify the effectiveness of the achieved method.