Mittag-Leffler stability of impulsive fractional-order systems

Wu, Ranchao; Hei, Xindong

doi:10.14232/ejqtde.2014.1.32

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Then the Stability Properties Of Zero Solution Of System (31

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“…Note that it is already stable, so it is asymptotically stable. Now consider the following one-dimensional linear impulsive fractional system [43] …”

Section: Then the Stability Properties Of Zero Solution Of System (3mentioning

confidence: 99%

“…In [41,42], stability about impulsive functional systems of fractional order was investigated. In [43], the algebraic stability of impulsive fractional-order systems was investigated and conditions ensuring stability were derived by Lyapunov method. Based on the stability theory, control of fractional-order systems could be realized, such as stabilization and synchronization.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of impulsive fractional-order systems by vector comparison principle

Fečkan

2015

Nonlinear Dyn

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Stability of impulsive fractional-order systems is investigated in this paper. By Lyapunov direct method and vector comparison principles, results about asymptotic stability are obtained. To this end, comparison principles, including scalar and vector forms, are generalized to impulsive fractional-order systems, through which fractional inequalities are derived for the linear impulsive systems. Then, based on such comparison principles, sufficient conditions for the MittagLeffler stability of impulsive fractional-order systems are established. Examples are given to show the effectiveness of the results.

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“…Note that it is already stable, so it is asymptotically stable. Now consider the following one-dimensional linear impulsive fractional system [43] …”

Section: Then the Stability Properties Of Zero Solution Of System (3mentioning

confidence: 99%