Approximate controllability of a semi-linear neutral evolution system with infinite delay

Mokkedem, Fatima Zahra; Fu, Xianlong

doi:10.1002/rnc.3619

Cited by 17 publications

(3 citation statements)

References 39 publications

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“…The differential expression of a neutral‐type system concludes not only the derivative term of the current state but also the derivative of the past state. () Many scholars have deeply investigated the stability and control problem of neutral‐type systems,() including approximate controllability, observer‐based control,()

H_{\infty}

control,() and reliable control. () Arino and Nosov studied the stability and asymptotic properties of a class of neutral‐type functional differential equations based on the pattern equation method.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Kao

Yang

Park

2017

Intl J Robust & Nonlinear

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In this paper, the exponential mean-square stability of neutral switching Markovian jump systems with generally incomplete transition probabilities is investigated. The model discussed in this paper concludes both deterministic switching signals and Markovian jumping signals. The transition rates of the jumping process are assumed to be partly available, that is, some elements have been exactly known, some have been merely known with lower and upper bounds, and others may have no information to use. Based on the Lyapunov-Krasovskii functional method, sufficient conditions on the exponential mean-square stability of the considered system are derived in terms of liner matrix inequalities. A numerical example is provided to show the feasibility and effectiveness of the proposed results.KEYWORDS exponential mean-square stability, generally uncertain transition rates, neutral-type Markovian jumping systems INTRODUCTIONNeutral-type systems play an important role in many branches of natural science and engineering science 1-3 because many practical delay systems could be modeled by neutral-type systems. The differential expression of a neutral-type system concludes not only the derivative term of the current state but also the derivative of the past state. 4,5 Many scholars have deeply investigated the stability and control problem of neutral-type systems, 6-9 including approximate controllability, 10 observer-based control, 11,12  ∞ control, 13-15 and reliable control. 16,17 Arino and Nosov 18 studied the stability and asymptotic properties of a class of neutral-type functional differential equations based on the pattern equation method.Int J Robust Nonlinear Control. 2018;28:1583-1596.wileyonlinelibrary.com/journal/rnc

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H_{\infty}

Section: Introductionmentioning

confidence: 99%

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Kao

Yang

Park

2017

Intl J Robust & Nonlinear

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“…Controllability analysis is used to solve a variety of real-world issues, such as issues with rocket launchers for satellite and aircraft control, issues with missiles and antimissile defense, and issues with managing the economy's infation rate. Over the last twenty years, a lot of work has been done for controllability of evolution equations [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability and Ulam Stability for Second-Order Impulsive Integrodifferential Evolution Equations with State-Dependent Delay

Bensalem,

Salim,

Benchohra

et al. 2024

International Journal of Differential Equations

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In this paper, we shall establish sufficient conditions for the existence, approximate controllability, and Ulam–Hyers–Rassias stability of solutions for impulsive integrodifferential equations of second order with state-dependent delay using the resolvent operator theory, the approximating technique, Picard operators, and the theory of fixed point with measures of noncompactness. An example is presented to illustrate the efficiency of the result obtained.

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“…It is therefore important to study this weaker version of controllability for nonlinear integrodifferential systems. Approximate controllability of nonlinear differential and integrodifferential systems with distributed controls, with and without delays in infinite dimensional spaces has been extensively studied (see e.g., [24,30,22,19,21,20,25,18] and the references contained in them).…”

mentioning

confidence: 99%

On the approximate boundary controllability of some partial functional integrodifferential equations with finite delay in Banach spaces

Ndambomve

Felix

2023

EECT

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<p style='text-indent:20px;'>This work concerns the study of approximate boundary controllability for some nonlinear partial functional integrodifferential equations with finite delay arising in the modeling of materials with memory, in the framework of general Banach spaces. We give sufficient conditions that ensure the approximate controllability of the system by supposing that its linear undelayed part is approximately controllable, admits a resolvent operator in the sense of Grimmer, and by making use of the Banach fixed-point Theorem and the continuity of the resolvent operator in the uniform norm-topology. As a result, we obtain a generalization of several important results in the literature, without assuming the compactness of the resolvent operator and the uniform boundedness of the nonlinear term. An example of applications is given for illustration.</p>

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Approximate controllability of a semi-linear neutral evolution system with infinite delay

Cited by 17 publications

References 39 publications

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Approximate Controllability and Ulam Stability for Second-Order Impulsive Integrodifferential Evolution Equations with State-Dependent Delay

On the approximate boundary controllability of some partial functional integrodifferential equations with finite delay in Banach spaces

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