Further research on exponential stability for quaternion-valued neural networks with mixed delays

Xu, Xiaolong; Xu, Quan; Yang, Jibin; Xue, Huanbin; Xu, Ye

doi:10.1016/j.neucom.2020.03.004

Cited by 22 publications

(16 citation statements)

References 40 publications

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“…In future works, we will extend the results to more general HMASs, such as fractional-order HMASs, HMASs with time delay, and cooperative-competitive interaction. At the same time, we will attempt to optimize control protocol and extend it to some other systems, i.e., fractional-order systems [48], memristive neural networks [49,50], and complex-valued neural networks [51,52].…”

Section: Discussionmentioning

confidence: 99%

Decentralized Adaptive Control for Quasi-Consensus in Heterogeneous Nonlinear Multiagent Systems

Yang

et al. 2021

Discrete Dynamics in Nature and Society

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This paper proposes some novel decentralized adaptive control protocols to settle the quasi-consensus problem of multiagent systems with heterogeneous nonlinear dynamics. Based on local communication with the leader and between the followers, some innovative control protocols are put forward to adapt the control gains and coupling weights simultaneously and to steer the consensus errors to some bounded areas. In particular, two new inequalities are proposed to establish the Lyapunov-based adaptive controller design approach for quasi-consensus. Some quasi-consensus criteria are derived by utilizing the designed controllers, in which the error bound can be modulated on the basis of the adaptive controller parameters. Numerical tests are conducted to show the feasibility of the theoretical derivation. Our findings highlight quasi-consensus in heterogeneous multiagent systems without adding some additional complex nonlinear control terms to cancel the dynamical differences between agents.

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Section: Discussionmentioning

confidence: 99%

Decentralized Adaptive Control for Quasi-Consensus in Heterogeneous Nonlinear Multiagent Systems

Yang

et al. 2021

Discrete Dynamics in Nature and Society

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“…Due to the appearance of the free variables included in the criteria, the obtained criteria theoretically seem to exhibit low conservatism. As pointed out by [45], in actual applications, finding the perfect combination of supposed parameters and incoming free variables depends to a large degree on performing incessant attempts. The judging matrixT -PL in Theorem 2 is just composed of assumption conditions including diffusion coefficients, self-feedback coefficients, connection matrices, and some assumed parameters for the activation functions, which is simple to apply in practice.…”

Section: Theoremmentioning

confidence: 99%

“…Besides of real-valued neural networks and CVNNs, an increasing number of studies are focusing on the quaternion-valued neural networks because of their advantages in aspect of image processing, unmanned aerial vehicle driving and recognition, human behavior recognition; see Refs. [45,46] and the references therein. The method applied in this paper and the work done in [45] demonstrate a potential route for further research, which will concentrate on the robust stability for a type of delayed quaternion-valued NNs with reaction-diffusion term.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

“…[45,46] and the references therein. The method applied in this paper and the work done in [45] demonstrate a potential route for further research, which will concentrate on the robust stability for a type of delayed quaternion-valued NNs with reaction-diffusion term.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

“…Due to the appearance of free variables within the proposed criteria, the conservatism of the criteria reduces theoretically. Nevertheless, as pointed out in [45], the perfect composition in real applications between the supposition-based parameters of the NNs and incoming free variables depends on experience and incessant attempts to a great degree. Without using LMI techniques, the scalar Lyapunov function method was applied to established some criteria for judging the stability of the corresponding RVNNs in [34,36,37,40,41] and CVNNs in [8-11, 13, 18].…”

Section: Introductionmentioning

confidence: 99%

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Exponential stability for delayed complex-valued neural networks with reaction-diffusion terms

Yang

et al. 2021

Adv Differ Equ

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In this study, we investigate reaction-diffusion complex-valued neural networks with mixed delays. The mixed delays include both time-varying and infinite distributed delays. Criteria are derived to ensure the existence, uniqueness, and exponential stability of the equilibrium state of the addressed system on the basis of the M-matrix properties and homeomorphism mapping theories as well as the vector Lyapunov function method. The results demonstrate the positive effect of reaction-diffusion on the stability, which further improves the existing conditions. Finally, the analysis of several examples is compared to the present results to verify the correctness and reduced conservatism of the primary results.

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Octonion short‐time linear canonical transform

Gao

2022

Math Methods in App Sciences

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We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.

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Further research on exponential stability for quaternion-valued neural networks with mixed delays

Cited by 22 publications

References 40 publications

Decentralized Adaptive Control for Quasi-Consensus in Heterogeneous Nonlinear Multiagent Systems

Decentralized Adaptive Control for Quasi-Consensus in Heterogeneous Nonlinear Multiagent Systems

Exponential stability for delayed complex-valued neural networks with reaction-diffusion terms

Octonion short‐time linear canonical transform

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