IEEE Trans Cybern. 2017 Oct;47(10):3184-3194. doi: 10.1109/TCYB.2017.2690676. Epub 2017 Apr 11.
This paper is concerned with the state estimation for neural networks with two additive time-varying delay components. Three cases of these two time-varying delays are fully considered: 1) both delays are differentiable uniformly bounded with delay-derivative bounded by some constants; 2) one delay is continuous uniformly bounded while the other is differentiable uniformly bounded with delay-derivative bounded by certain constants; and 3) both delays are continuous uniformly bounded. First, an extended reciprocally convex inequality is introduced to bound reciprocally convex combinations appearing in the derivative of some Lyapunov-Krasovskii functional. Second, sufficient conditions are derived based on the extended inequality for three cases of time-varying delays, respectively. Third, a linear-matrix-inequality-based approach with two tuning parameters is proposed to design desired Luenberger estimators such that the error system is globally asymptotically stable. This approach is then applied to state estimation on neural networks with a single interval time-varying delay. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.
本文研究了具有两个加性时变时滞分量的神经网络的状态估计问题。充分考虑了这两个时变时滞的三种情况：1）两个时滞都是可微的，一致有界，时滞导数由某些常数上界；2）一个时滞连续均匀有界，而另一个时滞可微均匀有界，时滞导数由某些常数上界；3）两个时滞都是连续均匀有界。首先，引入了一个扩展的互凸不等式，以限制出现在某些 Lyapunov-Krasovskii 泛函导数中的互凸组合。其次，基于扩展不等式，分别为三种时变时滞情况推导出了充分条件。第三，提出了一种基于线性矩阵不等式的方法，使用两个调谐参数设计期望的 Luenberger 估计器，以使误差系统全局渐近稳定。然后，将该方法应用于具有单个区间时变时滞的神经网络的状态估计。最后，给出了两个数值例子来说明所提出方法的有效性。
