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Abstract：
As with probability theory, uncertainty theory has been developed, in recent years, to portray indeterminacy phenomena in various application scenarios. We are concerned, in this paper, with the convergence property of state trajectories to equilibrium states (or fixed points) of time delayed uncertain cellular neural networks driven by the Liu process. By applying the classical Banach\'s fixed-point theorem, we prove, under certain conditions, that the delayed uncertain cellular neural networks, concerned in this paper, have unique equilibrium states (or fixed points). By carefully designing a certain Lyapunov-Krasovskii functional, we provide a convergence criterion, for state trajectories of our concerned uncertain cellular neural networks, based on our developed Lyapunov-Krasovskii functional. We demonstrate under our proposed convergence criterion that the existing equilibrium states (or fixed points) are exponentially stable almost surely, or equivalently that state trajectories converge exponentially to equilibrium states (or fixed points) almost surely. We also provide an example to illustrate graphically and numerically that our theoretical results are all valid. There seem to be rare results concerning the stability of equilibrium states (or fixed points) of neural networks driven by uncertain processes, and our study in this paper would provide some new research clues in this direction. The conservatism of the main criterion obtained in this paper is reduced by introducing quite general positive definite matrices in our designed Lyapunov-Krasovskii functional.
摘要：
和概率论一样,不确定性理论已经发展起来，近年来,描绘各种应用场景中的不确定性现象。我们关注,在本文中，具有状态轨迹对Liu过程驱动的时滞不确定细胞神经网络平衡态（或固定点）的收敛性。通过应用经典的Banach不动点定理，我们证明,在一定条件下,延迟的不确定细胞神经网络，在本文中，具有唯一的平衡态(或固定点)。通过精心设计某个Lyapunov-Krasovskii函数，我们提供了一个收敛标准，对于我们相关的不确定细胞神经网络的状态轨迹，基于我们开发的Lyapunov-Krasovskii函数。在我们提出的收敛准则下，我们证明了现有的平衡态（或固定点）几乎肯定是指数稳定的，或者等效地，状态轨迹几乎肯定地指数收敛到平衡态（或固定点）。我们还提供了一个例子，以图形和数字方式说明我们的理论结果都是有效的。关于由不确定过程驱动的神经网络的平衡态（或固定点）的稳定性，本文的研究将为这一方向提供一些新的研究线索。通过在我们设计的Lyapunov-Krasovskii函数中引入相当一般的正定矩阵，减少了本文获得的主要准则的保守性。
