Finite-time stability of impulsive fractional-order systems with time-delay

Hei, Xindong; Wu, Ranchao

doi:10.1016/j.apm.2015.11.012

Cited by 39 publications

(20 citation statements)

References 11 publications

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“…From practical considerations, FTS seems to be more appropriate for systems whose variables must lie within specific bounds. The problem of FTS of fractional‐order systems with time delay was considered in [8, 28, 31–33]. Proposition 5 Assume that matrices

falsefalse{C_{m} falsefalse}, C \in {double-struckC}^{n \times n}

are invertible and

\lim_{m false\to \infty} | | C_{m} - C | | = 0

.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Stability analysis of fractional differential time‐delay equations

Thành

Trinh

Phát

2017

IET Control Theory & Applications

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falsefalse{C_{m} falsefalse}, C \in {double-struckC}^{n \times n}

are invertible and

\lim_{m false\to \infty} | | C_{m} - C | | = 0

.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Stability analysis of fractional differential time‐delay equations

Thành

Trinh

Phát

2017

IET Control Theory & Applications

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“…In [9], the authors investigated the stability in finite range of time for the system of fractional order with delay equation by make use of the Mittag-Leffler delay type matrix. Hei and Wu [6] analyzed the stability in finite range of time for the fractional impulsive systems with delay by proposed few conditions. By utilizing generalized GI, FTS for the time delayed systems with FO have been proposed in [8], also the FTS analyzed for nonlinear system of FO in [14].…”

Section: Introductionmentioning

confidence: 99%

Finite-time stability of nonlinear fractional systems with damping behavior

Arthi¹,

Brindha²

2020

Malaya J. Mat

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“…In particular, FTS of linear fractional delay differential equations with controls was offered in Lazarević, and an inequality of Gronwall type is used to derive the results. For other related contribution, one can refer to previous works . However, an initial singular condition for the Riemann‐Liouville fractional differential equations is much different from the standard initial condition for a Caputo fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Finite time stability and relative controllability of Riemann‐Liouville fractional delay differential equations

Wang

2019

Math Methods in App Sciences

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This paper firstly deals with finite time stability (FTS) of Riemann-Liouville fractional delay differential equations via giving a series of properties of delayed matrix function of Mittag-Leffler. We secondly study relative controllability of such type-controlled system. With the help of the representation of solution, both Gram-like type matrix and rank criterion are derived, which extend the corresponding results for linear systems. KEYWORDSdelayed matrix function of Mittag-Leffler, finite time stability, fractional delay differential equations, relative controllability INTRODUCTIONRecently, some authors apply delayed exponential matrix function to find the explicit solution formula of linear delay equations. 1-3 Further, there are some continued work on finding the representation of solutions to delay continuous and discrete systems; see, for example, previous studies. [4][5][6][7][8][9][10][11] Fractional differential equations have been used in solving the practical problems in the fields of natural science. 12,13 In particular, FTS of linear fractional delay differential equations with controls was offered in Lazarević, 14 and an inequality of Gronwall type is used to derive the results. For other related contribution, one can refer to previous works. [15][16][17][18][19][20][21][22][23][24][25] However, an initial singular condition for the Riemann-Liouville fractional differential equations is much different from the standard initial condition for a Caputo fractional differential equations. The main results of the standard initial condition for a Caputo fractional delay differential equation were obtained in Li and Wang. 11 Relative controllability and its related problems of linear systems represented by different type delay systems have been studied in literature. [26][27][28][29][30][31][32][33] In particular, rank and Kalman criteria for relative controllability are studied extensively.Very recently, Li and Wang 12 studiedHere, D − + x denotes Riemann-Liouville fractional derivative, I 1− − + x denotes Riemann-Liouville fractional integral, T = k * < ∞ for a fixed k * ∈ {1, 2, … }, is a constant, ∈ C([− , T], R n ), and (D − + )( ) exists. We consider the Riemann-Liouville fractional derivative D − + , where the lower limit is − + (− is a singular point). To keep the "consistence" with the lower limit in Riemann-Liouville derivative, we keep the initial condition at − + .

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Finite-time stability of impulsive fractional-order systems with time-delay

Cited by 39 publications

References 11 publications

Stability analysis of fractional differential time‐delay equations

Stability analysis of fractional differential time‐delay equations

Finite-time stability of nonlinear fractional systems with damping behavior

Finite time stability and relative controllability of Riemann‐Liouville fractional delay differential equations

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