Robust Exponential Stability of Large-Scale System With Mixed Input Delays and Impulsive Effect

Xue, Huanbin; Zhang, Jiye; Zheng, Wei Xing; Wang, Hong

doi:10.1115/1.4033253

Cited by 8 publications

(3 citation statements)

References 17 publications

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“…The switching law, also known as the switching signal, determines which subnetwork is activated at any instant of time in the evolution of the system. As we all know, time delays are inevitable in electronic implementation of neural networks which usually degrades the performances of the models and the stability of the models may even be destroyed with the increase of delays (Xue and Zhang, 2017, 2019; Xue et al , 2016). Owing to the large number of parallel pathways with different axon sizes and lengths, neural networks usually have spatial properties.…”

Section: Introductionmentioning

confidence: 99%

Robust stability analysis of switched grey neural network models with distributed delays over C

Zhang

Xue

et al. 2022

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PurposeThe purpose of this paper is to study the dynamic behavior of complex-valued switched grey neural network models (SGNMs) with distributed delays when the system parameters and external input are grey numbers.Design/methodology/approachFirstly, by using the properties of grey matrix, M-matrix theory and Homeomorphic mapping, the existence and uniqueness of equilibrium point of the SGNMs were discussed. Secondly, by constructing a proper Lyapunov functional and using the average dwell time approach and inequality technique, the robust exponential stability of the SGNMs under restricted switching was studied. Finally, a numerical example is given to verify the effectiveness of the proposed results.FindingsSufficient conditions for the existence and uniqueness of equilibrium point of the SGNMs have been established; sufficient conditions for guaranteeing the robust stability of the SGNMs under restricted switching have been obtained.Originality/value(1) Different from asymptotic stability, the exponential stability of SGNMs which include grey parameters and distributed time delays will be investigated in this paper, and the exponential convergence rate of the SGNMs can also be obtained; (2) the activation functions, self-feedback coefficients and interconnected matrices are with different forms in different subnetworks; and (3) the results obtained by LMIs approach are complicated, while the proposed sufficient conditions are straightforward, which are conducive to practical applications.

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Section: Introductionmentioning

confidence: 99%

Robust stability analysis of switched grey neural network models with distributed delays over C

Zhang

Xue

et al. 2022

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“…This implies that the node subsystem and the link subsystem are the two main parts of dynamical behavior of complex network. On the other hand, stability analysis is the important problem in the study of complex dynamical networks, which has been extensively studied for the valueweighted complex dynamical networks, [6][7][8][9][10]16 the large scale systems, [17][18][19][20] and dynamical neural networks [21][22][23][24][25] in the last decades. However, if observing the results in the above literature from the angle of large-scale system, it is noticed that the stability is regarded only as the dynamical behavior of node subsystem, and the dynamical behavior of link subsystem is ignored.…”

Section: Introductionmentioning

confidence: 99%

Asymptotical stability for complex dynamical networks via link dynamics

Zhao

Wang

2020

Math Methods in App Sciences

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From the perspective of large‐scale system, a complex dynamical network can be regarded as the interconnected system with the node subsystem and link subsystem, which implies that the node subsystem and the link subsystem are the two main bodies of dynamical behaviors of network. Therefore, the whole stability of network is influenced by not only the dynamics of node subsystem but also the dynamics of link subsystem. According to the above view, the wholly asymptotical stability (WAS) is defined in this paper for the complex dynamical network with the model of differential equations. The WAS is used to describe the node subsystem achieves asymptotical stability when link subsystem achieves also the asymptotic stability in Lyapunov sense. For the WAS of the complex dynamical network, the corresponding criteria are derived by checking whether certain matrices are Hurwitz. The analysis results show that even if the isolated nodes are not asymptotically stable in Lyapunov sense, employing the dynamics of link can also force the node subsystem to achieve the asymptotical stability. Finally, the simulation examples show the validity of methods in this paper.

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“…Furthermore, from the point of view of control, multicontroller switching is an effective way to deal with complex systems. It is well-known that time delays are inevitable in a practical control design which usually leads to unsatisfactory performances and the stability of the dynamic systems may even be destroyed with the increase of delays [30][31][32][33][34][35]. Attributing to the interaction among the discrete dynamics, continuous dynamics, and time delays, the behaviors of delayed SNNs are very complicated.…”

Section: Introductionmentioning

confidence: 99%

Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

Xue

Peng

et al. 2018

Complexity

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In this paper, the stability of switched neural networks (SNNs) with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature.

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Robust Exponential Stability of Large-Scale System With Mixed Input Delays and Impulsive Effect

Cited by 8 publications

References 17 publications

Robust stability analysis of switched grey neural network models with distributed delays over C

Robust stability analysis of switched grey neural network models with distributed delays over C

Asymptotical stability for complex dynamical networks via link dynamics

Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

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