H∞ Performance State Estimation for Static Neural Networks With Time-Varying Delays via Two Improved Inequalities

This brief studies the problem of H-infinity 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-infinity 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.

Automated summary

This study presents an improved solution to the problem of H-infinity performance state estimation for static neural networks with time-varying delays. By deriving a less conservative criterion and designing estimator gain matrices independent of activation function, the effectiveness of the estimation method has been improved. This approach eliminates the constraint of having invertible activation functions, as compared to existing works.