Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods

Song, Meimei; Geng, Yidan; Liu, Mingzhu

doi:10.1016/j.amc.2020.125813

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…e investigation of RNNs subject to piecewise arguments is a breakthrough in literature [14], and the sufficient conditions for the exponential stability of a class of RNNs with piecewise arguments are given by constructing Lyapunov functions. At present, there are also some literatures further exploring the properties of the systems equipped with piecewise arguments [15,25,26]. On the other hand, it can be found that the parameter-intensity of the connection weight matrix is a crucial index affecting the stability of the systems [16-21, 27, 28].…”

Section: Introductionmentioning

confidence: 99%

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

Xie

2021

Complexity

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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.

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Section: Introductionmentioning

confidence: 99%

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

Xie

2021

Complexity

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“…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%

“…Ref. [53] considered the pth moment exponential stability equivalence among the stochastic differential equations and its derivative systems by the Euler-Maruyama method. In addition, Ref.…”

Section: Introductionmentioning

confidence: 99%

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

Xie

2021

IEEE Access

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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.

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Stability equivalence between regime‐switching jump diffusion delayed systems and corresponding systems with piecewise continuous arguments and application to discrete‐time feedback control

Liu,

Cheng,

Cai

2024

Asian Journal of Control

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In this paper, we mainly study the equivalence of exponential stability for regime‐switching jump diffusion delayed systems (RSJDDSs) and RSJDDSs with piecewise continuous arguments (RSJDDSs‐PCA). Our results show that if one of the RSJDDS and the RSJDDS‐PCA is th moment exponentially stable, then another system is also th moment exponentially stable when time delay and segment step size have a common upper bound, while both equations are almost surely exponentially stable, and we also provided a method to calculate this upper bound. In addition, as an application of the stability equivalence theorem, we design discrete‐time state and mode observations feedback control to stabilize unstable RSJDDSs and investigate that controllers of the drift, diffusion, and jump terms are all able to play a stabilizing effect on the controlled system.

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Stability equivalence among stochastic differential equations and stochastic differential equations with piecewise continuous arguments and corresponding Euler-Maruyama methods

Cited by 4 publications

References 26 publications

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

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

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

Stability equivalence between regime‐switching jump diffusion delayed systems and corresponding systems with piecewise continuous arguments and application to discrete‐time feedback control

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