IEEE Trans Neural Netw Learn Syst. 2017 Aug;28(8):1840-1850. doi: 10.1109/TNNLS.2016.2552491. Epub 2016 May 9.
This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.
本文研究了具有区间时变时滞的马尔可夫跳跃广义神经网络的渐近稳定性问题。马尔可夫跳跃参数被建模为一个连续时间和有限状态的马尔可夫链。通过构造一个合适的李雅普诺夫-克拉索夫斯基泛函（LKF），并利用线性矩阵不等式（LMI）形式，建立了新的时滞相关稳定性条件，以确定平衡点的均方渐近稳定性结果。互凸组合技术、 Jensen 不等式和基于 Wirtinger 的双积分不等式被用来处理 LKF 时导数中的单个和双积分项。所提出的结果由 LMI 表示。通过五个数值实例来说明新设计方法的有效性和优点。
