Neuronal State Estimation for Neural Networks With Two Additive Time-Varying Delay Components
研究了具有两个加性时变延迟的神经网络状态估计问题，针对三种延迟情况，利用扩展的互反凸不等式和LMI方法设计Luenberger估计器，使误差系统全局渐近稳定。
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.