Comments on “Lyapunov stability theorem about fractional system without and with delay”

Naifar, Omar; Makhlouf, Abdellatif Ben; Hammami, Mohamed

doi:10.1016/j.cnsns.2015.06.027

Cited by 41 publications

(18 citation statements)

References 2 publications

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“…It is worth mentioning that the authors in [19] have also proposed a direct Lyapunov stable theorem for fractional-order time-delay system (33). However, as pointed out in [20], their proof is not correct.…”

Section: Remarkmentioning

confidence: 95%

Disturbance Rejection for Fractional-Order Time-Delay Systems

Hai-peng

Liu

2016

Mathematical Problems in Engineering

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This paper presents an equivalent-input-disturbance (EID-) based disturbance rejection method for fractional-order time-delay systems. First, a modified state observer is applied to reconstruct the state of the fractional-order time-delay plant. Then, a disturbance estimator is designed to actively compensate for the disturbances. Under such a construction of the system, by constructing a novel monochromatic Lyapunov function and using direct Lyapunov approach, the stability analysis and controller design algorithm are derived in terms of linear matrix inequality (LMI) technique. Finally, simulation results demonstrate the validity of the proposed method.

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Section: Remarkmentioning

confidence: 95%

Disturbance Rejection for Fractional-Order Time-Delay Systems

Hai-peng

Liu

2016

Mathematical Problems in Engineering

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“…For example, electromagnetic systems [7] and financial systems [8] have been successfully modeled using fractional-order calculus. Note that, in recent years, the use of fractional-order equations in stability theory has gained momentum [9,10]. Dealing with the observer design query for nonlinear fractional-order systems, it can be regarded as a fertile area of research, compared to the integer-order case.…”

Section: Introductionmentioning

confidence: 99%

State estimation for nonlinear conformable fractional‐order systems: A healthy operating case and a faulty operating case

Jmal¹,

Elloumi

Naifar³

et al. 2019

Asian Journal of Control

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The issue of estimating states for classical integer‐order nonlinear systems has been widely addressed in the literature. Yet, generalization of existing results to the fractional‐order framework represents a fertile area of research. Note that, recently, a new and advantageous type of fractional derivative, the conformable derivative, was defined. So far, the general query of designing observers for conformable fractional‐order systems has not been investigated. In addition, it has been proved in the literature that some important tools for stability analysis of fractional‐order systems are valid using the conformable derivative concept, but invalid using other fractional derivative concepts. Motivated by the cited facts, this paper presents a first‐state estimation scheme for fractional‐order systems under the conformable derivative concept. A healthy operating case and a faulty operating case are treated. In this paper, a version of Barbalat's lemma, which is invalid using the well‐known Caputo derivative, is exploited to prove the convergence of the estimation errors. In order to validate the theoretical results, a numerical example is studied in the simulation section.

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“…Fractional differential systems appear naturally in numerous fields such as electromagnetic systems, economy, image processing and physics, see . Moreover, science and complex engineering systems have significantly stimulated using the fractional calculus in many issues of control theory, such as stability . A. Ben Makhlouf et al treated the stability of fractional‐order nonlinear systems depending on a parameter.…”

Section: Introductionmentioning

confidence: 99%

Finite‐Time Stability of Linear Caputo‐Katugampola Fractional‐Order Time Delay Systems

Makhlouf

Nagy

2018

Asian Journal of Control

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In this paper, a finite-time stability procedure is suggested for a class of Caputo-Katugampola fractional-order time delay systems. Sufficient conditions are derived to prove this fact. Numerical results are provided to demonstrate the validity of our theoretical results. 302 Color figure can be viewed at wileyonlinelibrary.com [ ] Color figure can be viewed at wileyonlinelibrary.com [ ] Fig. 6. The norm of the state vector of (13) at = 1 (up) and = 0.5 (down) when = 0.4, respectively.

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Comments on “Lyapunov stability theorem about fractional system without and with delay”

Cited by 41 publications

References 2 publications

Disturbance Rejection for Fractional-Order Time-Delay Systems

Disturbance Rejection for Fractional-Order Time-Delay Systems

State estimation for nonlinear conformable fractional‐order systems: A healthy operating case and a faulty operating case

Finite‐Time Stability of Linear Caputo‐Katugampola Fractional‐Order Time Delay Systems

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