School of Electrical Engineering and Automation, Hubei Normal University, Huangshi 435002, China; School of information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, China.
School of information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, China.
ISA Trans. 2022 Oct;129(Pt A):179-192. doi: 10.1016/j.isatra.2021.11.046. Epub 2021 Dec 15.
In this paper, we are concerned with the multimode function multistability for Cohen-Grossberg neural networks (CGNNs) with mixed time delays. It is introduced the multimode function multistability as well as its specific mathematical expression, which is a generalization of multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and asymptotic stability. Also, according to the neural network (NN) model and the maximum and minimum values of activation functions, n pairs of upper and lower boundary functions are obtained. Via the locations of the zeros of the n pairs of upper and lower boundary functions, the state space is divided into ∏(2H+1) parts correspondingly. By virtue of the reduction to absurdity, continuity of function, Brouwer's fixed point theorem and Lyapunov stability theorem, the criteria for multimode function multistability are acquired. Multiple types of multistability, including multiple exponential stability, multiple polynomial stability, multiple logarithmic stability, and multiple asymptotic stability, can be achieved by selecting different types of function P(t). Two numerical examples are offered to substantiate the generality of the obtained criteria over the existing results.
本文研究了具有混合时滞的 Cohen-Grossberg 神经网络（CGNNs）的多模函数多稳定性。引入了多模函数多稳定性及其具体的数学表达式，这是对多个指数稳定性、多个多项式稳定性、多个对数稳定性和渐近稳定性的推广。此外，根据神经网络（NN）模型和激活函数的最大值和最小值，得到了 n 对上下边界函数。通过 n 对上下边界函数的零点位置，相应地将状态空间划分为∏(2H+1)个部分。通过反证法、函数连续性、Brouwer 不动点定理和 Lyapunov 稳定性定理，得到了多模函数多稳定性的准则。通过选择不同类型的函数 P(t)，可以实现多种类型的多稳定性，包括多个指数稳定性、多个多项式稳定性、多个对数稳定性和多个渐近稳定性。通过两个数值例子验证了所得到的准则相对于现有结果的通用性。
