Department of Automation, Zhejiang University of Technology, Zhejiang Provincial United Key Laboratory of Embedded Systems, Hangzhou, PR China.
Neural Netw. 2012 Nov;35:103-11. doi: 10.1016/j.neunet.2012.08.005. Epub 2012 Aug 31.
This paper is concerned with the exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays. The parameters of the neural networks are subject to the switching from one mode to another according to a Markov chain. By constructing a novel Lyapunov-Krasovskii functional and developing a new convex combination technique, a new delay-dependent exponential stability condition is proposed, such that for all admissible delay bounds, the resulting estimation error system is mean-square exponentially stable with a prescribed noise attenuation level in the H(∞) sense. It is also shown that the design of the desired state estimator is achieved by solving a set of linear matrix inequalities (LMIs). The obtained condition implicitly establishes the relations among the maximum delay bounds, H(∞) noise attenuation level and the exponential decay rate of the estimation error system. Finally, a numerical example is given to show the effectiveness of the proposed result.
本文研究了具有时变离散和分布时滞的马尔可夫跳变神经网络的指数状态估计问题。神经网络的参数根据马尔可夫链从一种模式切换到另一种模式。通过构造一个新的李雅普诺夫-克拉索夫斯基泛函，并采用一种新的凸组合技术，提出了一个新的时滞相关指数稳定性条件，使得对于所有可允许的时滞界，所得到的估计误差系统在 H(∞)意义下具有给定的噪声衰减水平的均方指数稳定性。还表明，通过求解一组线性矩阵不等式 (LMI)，可以实现期望状态估计器的设计。所得到的条件隐含地建立了最大时滞界、H(∞)噪声衰减水平和估计误差系统指数衰减率之间的关系。最后，通过一个数值例子验证了所提出结果的有效性。
