Discrete feedback control for highly nonlinear neutral stochastic delay differential equations with Markovian switching

Mei, Chunhui; Fei, Chen; Shen, Mingxuan; Fei, Weiyin; Mao, Xuerong

doi:10.1016/j.ins.2022.01.027

Cited by 15 publications

(16 citation statements)

References 35 publications

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“…• New stabilization theories are established based on Lyapunov functionals. In addition to the stability results in [35] and [24], this paper also proves the almost surely asymptotic stability of the solution of the controlled HNSNMJS.…”

Section: Introductionsupporting

confidence: 53%

“…The Lyapunov-type criteria established in [35] cannot be used to discuss the ES for the controlled HNSNMJSs. In [24], the exponential stabilization of HNSNMJSs based on the discrete state observations is studied. Here, the system considered has only a single delay.…”

Section: Theoremmentioning

confidence: 99%

“…The SNMJDSs with highly nonlinear coefficients (referred to below as highly nonlinear stochastic neutral Markovian jump systems (HNSNMJSs)) are certainly studied (see e.g., [20][21][22][23][24][25]). Most of the existing results are for the case containing only one retarded derivative of the state.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Shen et al [35] developed new theories on the asymptotic stabilization for HNSNMJSs. Mei et al [24] realized the exponential stabilization of controlled HNSNMJSs. However, by studying these two excellent works, one can find that both of them focused on HNSNMJSs with only a single delay and did not consider asymptotic stabilization and exponential stabilization synthetically.…”

Section: Introductionmentioning

confidence: 99%

“…• The HNSNMJS discussed in this paper contains multiple delays in the neutral term, which is more general and practical than those studied in [24,30,35]. New mathematical techniques are developed to deal with these complex situations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stabilization of highly nonlinear stochastic neutral Markovian jump systems with multiple delays

Fan

Park

et al. 2022

IET Control Theory & Appl

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This paper is concerned with the stabilization of highly nonlinear stochastic neutral Markovian jump systems (HNSNMJSs) with multiple delays. First, mild conditions are imposed on the coefficients of the system to ensure the existence and uniqueness of the solution. Second, the design method of the delayed feedback control is provided to stabilize an unstable HNSNMJS with multiple delays in the neutral term. In particular, novel conditions in terms of M-matrices are proposed for the control function, which facilitate derivation and calculation and are easy to verify. Then, by applying Lyapunov functional-based approach, new theories on the asymptotic stabilization and exponential stabilization are established. Finally, the validity of the theoretical results is illustrated through a numerical example.

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Section: Introductionsupporting

confidence: 53%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stabilization of highly nonlinear stochastic neutral Markovian jump systems with multiple delays

Fan

Park

et al. 2022

IET Control Theory & Appl

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A note on the general stabilization of discrete feedback control for non-autonomous hybrid neutral stochastic systems with a delay

Feng,

Zhang,

Cao

et al. 2024

Acta Math Sci

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Exponential Stability of Impulsive Stochastic Neutral Neural Networks with Lévy Noise Under Non-Lipschitz Conditions

Ma,

Li,

Liu

et al. 2024

Neural Process Lett

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In this paper, the exponential stability issue of stochastic impulsive neutral neural networks driven by Lévy noise is explored. By resorting to the Lyapunov-Krasovskii function that involves neutral time-delay components, the properties of the Lévy process, as well as various inequality approaches, some sufficient exponential stability criteria in non-Lipschitz cases are obtained. Besides, the achieved results depend on the time-delay, noise intensity, and impulse factor. At the end of the paper, two numerical examples with simulations are presented to demonstrate the effectiveness and feasibility of the addressed results

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Discrete feedback control for highly nonlinear neutral stochastic delay differential equations with Markovian switching

Cited by 15 publications

References 35 publications

Stabilization of highly nonlinear stochastic neutral Markovian jump systems with multiple delays

Stabilization of highly nonlinear stochastic neutral Markovian jump systems with multiple delays

A note on the general stabilization of discrete feedback control for non-autonomous hybrid neutral stochastic systems with a delay

Exponential Stability of Impulsive Stochastic Neutral Neural Networks with Lévy Noise Under Non-Lipschitz Conditions

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