Guaranteed $H_{\infty}$ Performance State Estimation of Delayed Static Neural Networks

Abstract

This brief studies the guaranteed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance state estimation problem of delayed static neural networks. The single- and double-integral terms in the time derivative of the Lyapunov functional are handled by the reciprocally convex combination and a new integral inequality, respectively. A delay-dependent design criterion is established such that the error system is globally exponentially stable with a decay rate and a prescribed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance is guaranteed. The gain matrix and the optimal performance index are obtained via solving a convex optimization problem subject to linear matrix inequalities. A numerical example is exploited to demonstrate that much better performance can be achieved by this approach.