Lin Wen-Juan, He Yong, Zhang Chuan-Ke, Wu Min
IEEE Trans Neural Netw Learn Syst. 2020 Dec;31(12):5456-5467. doi: 10.1109/TNNLS.2020.2968074. Epub 2020 Nov 30.
In this article, the finite-time H state estimation problem is addressed for a class of discrete-time neural networks with semi-Markovian jump parameters and time-varying delays. The focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite-time bounded with a prescribed H performance level via finite-time Lyapunov stability theory. By constructing a delay-product-type Lyapunov functional, in which the information of time-varying delays and characteristics of activation functions are fully taken into account, and using the Jensen summation inequality, the free weighting matrix approach, and the extended reciprocally convex matrix inequality, some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator. Finally, numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results.
本文针对一类具有半马尔可夫跳变参数和时变延迟的离散时间神经网络，研究了有限时间H状态估计问题。重点主要在于状态估计器的设计，使得通过有限时间李雅普诺夫稳定性理论，构造的误差系统在规定的H性能水平下是随机有限时间有界的。通过构造一个充分考虑时变延迟信息和激活函数特性的延迟积型李雅普诺夫泛函，并利用詹森求和不等式、自由加权矩阵方法和扩展的互易凸矩阵不等式，以线性矩阵不等式的形式建立了一些充分条件，以确保状态估计器的存在。最后，给出了数值例子和仿真结果，以说明所提结果的有效性。
