IEEE Trans Cybern. 2017 Oct;47(10):3040-3049. doi: 10.1109/TCYB.2017.2665683. Epub 2017 Feb 17.
This paper is concerned with the stability analysis of discrete-time neural networks with a time-varying delay. Assessment of the effect of time delays on system stability requires suitable delay-dependent stability criteria. This paper aims to develop new stability criteria for reduction of conservatism without much increase of computational burden. An extended reciprocally convex matrix inequality is developed to replace the popular reciprocally convex combination lemma (RCCL). It has potential to reduce the conservatism of the RCCL-based criteria without introducing any extra decision variable due to its advantage of reduced estimation gap using the same decision variables. Moreover, a delay-product-type term is introduced for the first time into the Lyapunov function candidate such that a delay-variation-dependent stability criterion with the bounds of delay change rate is established. Finally, the advantages of the proposed criteria are demonstrated through two numerical examples.
本文研究了时变时滞离散时间神经网络的稳定性分析。评估时滞对系统稳定性的影响需要合适的时滞相关稳定性准则。本文旨在开发新的稳定性准则，以减少保守性，而不会增加太多的计算负担。本文提出了一种扩展的互凸矩阵不等式，以替代流行的互凸组合引理（RCCL）。由于其利用相同决策变量减少估计间隙的优势，因此有可能减少基于 RCCL 的准则的保守性，而不会引入任何额外的决策变量。此外，首次在李雅普诺夫函数候选者中引入了延迟积型项，从而建立了具有延迟变化率边界的延迟相关稳定性准则。最后，通过两个数值示例验证了所提出准则的优点。
