A novel Mittag–Leffler stable estimator for nonlinear fractional-order systems: a linear quadratic regulator approach

Martínez-Fuentes, Óscar; Martínez-Guerra, Rafael

doi:10.1007/s11071-018-4469-6

Cited by 19 publications

(4 citation statements)

References 41 publications

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“…In [60,57], a new class of observers for fractional-order systems is introduced. These observers, called Mittag-Leffler observers, satisfy the conditions 1 and 2 previously mentioned.…”

Section: Mittag-leffler Observersmentioning

confidence: 99%

Stability of Fractional Nonlinear Systems with Mittag-Leffler Kernel and Design of State Observers

Martínez-Fuentes,

Delfín-Prieto

2020

Preprint

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Atangana and Baleanu proposed a new fractional derivative with non-local and nosingular MittagLeffler kernel to solve some problems proposed by researchers in the field of fractional calculus. This new derivative is better to describe essential aspects of non-local dynamical systems. We present some results regarding Lyapunov stability theory, particularly the Lyapunov Direct Method for fractional-order systems modeled with Atangana-Baleanu derivatives and some significant inequalities that help to develop the theoretical analysis. As applications in control theory, some algorithms of state estimation are proposed for linear and nonlinear fractional-order systems.

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“…In [60,57], a new class of observers for fractional-order systems is introduced. These observers, called Mittag-Leffler observers, satisfy the conditions 1 and 2 previously mentioned.…”

Section: Mittag-leffler Observersmentioning

confidence: 99%

Stability of Fractional Nonlinear Systems with Mittag-Leffler Kernel and Design of State Observers

Martínez-Fuentes,

Delfín-Prieto

2020

Preprint

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“…The finite time stability of delayed FOSs by Mittag-Leffler functions was analyzed in [28]. An MLS estimator for a nonlinear FOS using a linear quadratic regulator approach was studied in [29]. Many problems in viscoelasticity, acoustics, populations dynamics, electromagnetics, hydrology, chemical reactions and other areas can be modeled by fractional integro-differential equations; see [30][31][32] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays

Mathiyalagan

Zeng

Yavuz

2022

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In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffler stability (MLS) of the considered system are established by using well known mathematical techniques, and further, the two corollaries are deduced, which still gives some new results. Finally, an example is given to illustrate the applications of the results.

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“…The finite time stability of delayed FOSs by Mittag–Leffler functions was analyzed in Li and Wang ( 2018 ). MLS estimator for nonlinear FOS using linear quadratic regulator approach has been studied in Martnez-Fuentes and Martnez-Guerra ( 2018 ).…”

Section: Introductionmentioning

confidence: 99%

Mittag–Leffler Stability of Impulsive Nonlinear Fractional-Order Systems with Time Delays

Mathiyalagan

2022

Iran J Sci

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Stability analysis of impulsive nonlinear fractional-order system (FOS) is discussed. First, the existence and uniqueness of solutions for FOS is discussed with help of fixed point theory. The nonlinear system is considered with a constant time delay and impulsive effects. Then, novel sufficient conditions to prove the Mittag–Leffler stability (MLS) of FOS are established by using well known mathematical techniques. Also, the results are extended to present finite-time MLS conditions for considered nonlinear FOSs. Finally, examples are given to show the validity of the derived results.

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A novel Mittag–Leffler stable estimator for nonlinear fractional-order systems: a linear quadratic regulator approach

Cited by 19 publications

References 41 publications

Stability of Fractional Nonlinear Systems with Mittag-Leffler Kernel and Design of State Observers

Stability of Fractional Nonlinear Systems with Mittag-Leffler Kernel and Design of State Observers

Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays

Mittag–Leffler Stability of Impulsive Nonlinear Fractional-Order Systems with Time Delays

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