Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

Si, Wenxiao; Xie, Tao; Li, Biwen

doi:10.1155/2021/9941881

Cited by 7 publications

(11 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So the state of SNPNDS (33) achieves globally exponential stability. ---Shen2013 [25] --Shen2016 [26] --Wu2015 [27] --Zhang2017 [28] -Our recent work [29] --This paper (Note: The work in Part III includes the first five elements; and the work in Part IV includes all these six elements. )…”

Section: The Robustness Of Snpndsmentioning

confidence: 99%

“…Robustness and GES for nonlinear systems are two hot research fields no matter in the past or present [15], [16], [19], [20], [24]- [29]. On the one hand, robustness is usually endowed with different meanings in diverse application scenarios.…”

Section: Introductionmentioning

confidence: 99%

“…So far, with a view to these three kinds of interference factors: PCA, NT and SD, some investigators researched the robustness or GES of nonlinear systems influenced by single interference factor, such as [6], [20], [24], [25], [26], [30], [33], [50], etc. Some investigators explored the robustness or GES of systems affected by dual interference factors, such as [16], [27], [28], [29], [51], [53] and so forth. In the above literatures, Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, Ref. [20], [24]- [29] investigated the robustness of dynamical systems by deriving the upper bounds of the single interference factors [20], [24], [25], [26] or dual interference factors [27], [28], [29]. However, very few studies have been done to explore the RoGES of nonlinear systems subject to all these three interference factors.…”

Section: Introductionmentioning

confidence: 99%

“…Synthesize the above, in accordance with [29], we will further explore the RoGES of nonlinear dynamical system with piecewise constant arguments, neutral terms and stochastic disturbances (SNPNDS). (NPNDS is the system which removes the stochastic disturbances of SNPNDS).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robustness Analysis of Exponential Stability of Neutral-Type Nonlinear Systems With Multi-Interference

Xie

2021

IEEE Access

Self Cite

View full text Add to dashboard Cite

With a view to the unfavorable impact of the inevitable exogenous interferences for the practical engineering and signal transmission, here we focus on the robustness of global exponential stability for nonlinear dynamical system subject to piecewise constant arguments, neutral terms and stochastic disturbances (SNPNDS). A new troublesome problem is that the neutral terms appeared in the derivative part affected on the other two interference factors is not a simple accumulation, so the Lipchitz condition is adopted to establish the ternary transcendental equations. However, different from previous transcendental equations with single or double variables, solving the transcendental equations with three variables becomes the bottleneck again. Hence, the special independent parameters & interdependent variables method targeted for SNPNDS is adopted here: firstly, all relative independent parameters are fixed. Next, the upper bounds of these three interdependent variables are orderly derived by their coupling relationship. Therein, the optimal constraint conditions for piecewise constant arguments and neutral terms are deduced. Through the strategies mentioned above, a class of algebraic problems of estimating three upper bounds by solving transcendental equations with three variables is settled. Besides, the main method ensures the relationship built among the interference factors is mutually restrictive and dynamic. Meanwhile, the optimized constraints make the linkage effect more comprehensive and valid. Furthermore, the established mechanism is practical enough to be generalized to more multivariable systems. Finally, the numerical simulation comparisons are given to illustrate the validity of the derived results.INDEX TERMS Robustness, nonlinear system, neutral term, piecewise constant argument, stochastic disturbance.

show abstract

Section: The Robustness Of Snpndsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robustness Analysis of Exponential Stability of Neutral-Type Nonlinear Systems With Multi-Interference

Xie

2021

IEEE Access

Self Cite

View full text Add to dashboard Cite

show abstract

Further Results on Exponentially Robust Stability of Uncertain Connection Weights of Neutral-Type Recurrent Neural Networks

Xie

2021

Complexity

Self Cite

View full text Add to dashboard Cite

Further results on the robustness of the global exponential stability of recurrent neural network with piecewise constant arguments and neutral terms (NPRNN) subject to uncertain connection weights are presented in this paper. Estimating the upper bounds of the two categories of interference factors and establishing a measuring mechanism for uncertain dual connection weights are the core tasks and challenges. Hence, on the one hand, the new sufficient criteria for the upper bounds of neutral terms and piecewise arguments to guarantee the global exponential stability of NPRNN are provided. On the other hand, the allowed enclosed region of dual connection weights is characterized by a four-variable transcendental equation based on the preceding stable NPRNN. In this way, two interference factors and dual uncertain connection weights are mutually restricted in the model of parameter-uncertainty NPRNN, which leads to a dynamic evolution relationship. Finally, the numerical simulation comparisons with stable and unstable cases are provided to verify the effectiveness of the deduced results.

show abstract

Stability Analysis of Cohen–Grossberg Type BAM Neural Network with Piecewise Constant Argument

Zheng,

Xie,

Fang

2023

Discrete Dynamics in Nature and Society

Self Cite

View full text Add to dashboard Cite

This paper introduces the stability problems of Cohen–Grossberg type BAM neural network (BAMCGNN) with piecewise constant argument (PCA). By employing the homeomorphism theory, sufficient conditions for the existence and uniqueness of the equilibrium point are obtained; using inequality technique and Lyapunov method, sufficient stability criteria for BAMCGNN with PCA are presented. Finally, a numerical case shows the significance of the results of this paper.

show abstract

Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

Cited by 7 publications

References 37 publications

Robustness Analysis of Exponential Stability of Neutral-Type Nonlinear Systems With Multi-Interference

Robustness Analysis of Exponential Stability of Neutral-Type Nonlinear Systems With Multi-Interference

Further Results on Exponentially Robust Stability of Uncertain Connection Weights of Neutral-Type Recurrent Neural Networks

Stability Analysis of Cohen–Grossberg Type BAM Neural Network with Piecewise Constant Argument

Contact Info

Product

Resources

About