Sufficient Conditions of Interval Stability of a Class of Linear Impulsive Systems with a Delay

Слынько, В. И.; Tunç, Cemil; Erdur, Sultan

doi:10.1134/s1064230719060145

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…As is known to all, time delay exists widely in various practical systems. Many results have been made in the analysis of time-delay systems [11][12][13][14][15][16][17]33]. In recent years, the stability of impulsive delay differential equations has received much extensive attention from researchers.…”

Section: Introductionmentioning

confidence: 99%

Uniform Stability of Linear Delay Impulsive Differential Systems With Impulse Time Windows and Logic Choice

Hui,

Luo,

Wang

et al. 2023

IEEE Access

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This paper focuses on the uniform stability of linear delay impulsive differential systems with impulse time windows and logic choice. Firstly, a class of linear delay impulsive differential systems with impulse time windows and logic choice is constructed. The impulsive effects of this system have the following two properties: (i) The impulses do not appear at the fixed time points, but may occur at any points in a little range of time. (ii) The impulsive effects are affected by logic choice. Furthermore, by using the semi-tensor product method, we convert the logical functions contained in impulses into equivalent algebraic expressions. Next, based on Lyapunov functions and Razumikhin technique, the uniform stability criterion is obtained. Then, the uniform stability criterion is also applied to a class of linear uncertain delay impulsive differential systems with impulse time windows and logic choice. Finally, two illustrative examples are also discussed. INDEX TERMS Uniform stability; Impulsive differential systems; Impulse time windows; Logic choice; Semi-tensor product; Uncertain.

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Section: Introductionmentioning

confidence: 99%

Uniform Stability of Linear Delay Impulsive Differential Systems With Impulse Time Windows and Logic Choice

Hui,

Luo,

Wang

et al. 2023

IEEE Access

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“…From the perspective of the research topics on impulsive systems, in addition to periodic solutions [8], oscillation [9], noise [10], etc., various kinds of stability have also been studied extensively. For example, exponential stability [11], practical stability [12], interval stability [13], finitetime stability [14], numerical stability [15] and so on. From the perspective of the classification of impulsive systems, many research results have been reported for linear systems [9,11,13,16,17], nonlinear systems [18,19], functional differential systems [12,20,21], integro-differential systems [22], fractional differential systems [23,24] and so on.…”

Section: Introductionmentioning

confidence: 99%

“…For example, exponential stability [11], practical stability [12], interval stability [13], finitetime stability [14], numerical stability [15] and so on. From the perspective of the classification of impulsive systems, many research results have been reported for linear systems [9,11,13,16,17], nonlinear systems [18,19], functional differential systems [12,20,21], integro-differential systems [22], fractional differential systems [23,24] and so on. From the perspective of the model composition of the impulsive system, due to the needs of practical problems, time-delay and stochastic effects are often taken into account in the impulsive model.…”

Section: Introductionmentioning

confidence: 99%

“…From the perspective of the model composition of the impulsive system, due to the needs of practical problems, time-delay and stochastic effects are often taken into account in the impulsive model. Therefore, the delay impulsive systems such as [9,11,13,15,16,18,19,20,25,26], stochastic impulsive systems such as [27,28], and more complex stochastic delay impulsive systems such as [21,29] should be fully considered.…”

Section: Introductionmentioning

confidence: 99%

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Exponential Stability for a Class of Linear Delay Differential Systems Under Logic Impulsive Control

2021

IEEE Access

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This paper is concerned with the exponential stability for a class of linear delay differential systems under logic impulsive control. Based on logic impulsive control, the strong constraint that the coefficient functions of this kind of linear delay differential system need to be non-negative, which is required in most of the previous studies, is reduced. By establishing the relationship between the logic impulsive system and a corresponding non-impulsive system, some exponential stability criteria for linear delay differential systems under logic impulsive control are presented in the following two cases: Case A-The coefficient functions are non-negative, Case B-The coefficient functions can be negative. Two numerical examples are discussed to verify the results.

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Linear Periodic Systems

Church

Liu

2020

Bifurcation Theory of Impulsive Dynamical Systems

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Sufficient Conditions of Interval Stability of a Class of Linear Impulsive Systems with a Delay

Cited by 6 publications

References 17 publications

Uniform Stability of Linear Delay Impulsive Differential Systems With Impulse Time Windows and Logic Choice

Uniform Stability of Linear Delay Impulsive Differential Systems With Impulse Time Windows and Logic Choice

Exponential Stability for a Class of Linear Delay Differential Systems Under Logic Impulsive Control

Linear Periodic Systems

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