Almost Surely Exponential Convergence Analysis of Time Delayed Uncertain Cellular Neural Networks Driven by Liu Process via Lyapunov-Krasovskii Functional Approach

被引:1
|
作者
Wang, Chengqiang [1 ]
Jia, Zhifu [1 ]
Zhang, Yulin [2 ]
Zhao, Xiangqing [1 ]
Pernice, Riccardo
de Felice, Giulio
Antonacci, Yuri
机构
[1] Suqian Univ, Sch Math, Suqian 223800, Peoples R China
[2] Chengdu Normal Univ, Sch Math, Chengdu 611130, Peoples R China
关键词
cellular neural networks; Liu process; time delays; equilibrium states; convergence analysis; uncertainty theory; Lyapunov-Krasovskii functionals; ASYMPTOTIC STABILITY; DYNAMICAL-SYSTEMS; PTH MOMENT; CONSENSUS; JUMP;
D O I
10.3390/e25111482
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
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页数:28
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