Controllability and observability behaviors of a non-homogeneous conformable fractional dynamical system compatible with some electrical applications

Al–Zhour, Zeyad

doi:10.1016/j.aej.2021.07.018

Cited by 21 publications

(12 citation statements)

References 56 publications

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“…In this section, we give two examples are provided to illustrate the effectiveness of our results and compare it with literature in (Al-Zhour, 2022;Sadek et al, 2022) using Maple software.…”

Section: Examplesmentioning

confidence: 97%

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Controllability and observability for fractal linear dynamical systems

Sadek

2022

Journal of Vibration and Control

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In the present paper, we investigate the controllability, and observability of a non-homogeneous continuous-time fractal dynamical system (NC-TFDS). We show that the controllability is equivalent to a controllability matrix that has a full rank. We also show a relationship between controllability and fractal differential Lyapunov equation (F-DLE). We give some theorems for the observability of a NC-TFDS. Finally, we offer two examples are provided to illustrate the effectiveness of our results and compare it with the two papers Al-Zhour (2022) and ( Sadek et al., 2022 ).

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Section: Examplesmentioning

confidence: 97%

“…In this example, we consider example in [Al-Zhour, 2022;Sadek et al, 2022] to demonstrate the effectiveness of our results of the form 8 < :…”

Section: Examplesmentioning

confidence: 99%

Controllability and observability for fractal linear dynamical systems

Sadek

2022

Journal of Vibration and Control

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“…Additionally, the studies show multiple instances of the diffusion equation solution being unique in [32]. Some further additional efforts to the conformable derivative are recently done by researchers, for example, the multiagent systems with impulsive control protocols [33], numerical methods [34], time power-based grey model [35], multivariate grey system model [36], controllability and observability [37], the Barbalat lemma [38], and H∞ observers [39].…”

Section: Introductionmentioning

confidence: 99%

Global Practical Conformable Stabilization by Output Feedback for a Class of Nonlinear Fractional‐Order Systems

Gassara

Naifar

Makhlouf

et al. 2022

Mathematical Problems in Engineering

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Researchers have explored the concept of “practical stability” in the literature, pointing out that stability investigations always guarantee “practical stability” and the inverse is not true. The concept “practical stability” means that the origin is not an equilibrium point and the convergence of the system state is towards a ball centered at the origin. The primary purpose of this work is to investigate the notation of practical stability for a new class of fractional-order systems using the general conformable derivative. As a second objective, the nonlinear condition chosen is novel in that it is not Lipschitz as is customary, which is original in and of itself. In addition, some new analysis related to the LMI techniques was used to prove the main results. To begin, a method of stabilization is provided. Following that, the proposed system’s observer design is presented. Also, the principle of separation is described. Finally, a numerical example is offered to demonstrate the proposed methodology’s validity.

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“…In recent years, fractional diferential equations (FDEs) have found applications in many problems in physical. As in most of the time, these equations cannot be solved exactly except when we know some particular solutions or else we refer to the study of existence and uniqueness of solutions using some fundamental theorems of functional analysis (the Banach contraction theorem) for the other FDEs (Riemann-Liouville and Caputo) (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%

Practical Stability for Conformable Time-Delay Systems

Kharrat

Gassara

Rhaima

et al. 2023

Discrete Dynamics in Nature and Society

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This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm the practical exponential stability and design of the proposed class of systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These conditions are expressed in the form of linear matrix inequalities (LMI) which could be solved by using solvers in LMI Toolbox of MATLAB. Two numerical examples are given to illustrate the applicability of the proposed results.

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Controllability and observability behaviors of a non-homogeneous conformable fractional dynamical system compatible with some electrical applications

Cited by 21 publications

References 56 publications

Controllability and observability for fractal linear dynamical systems

Controllability and observability for fractal linear dynamical systems

Global Practical Conformable Stabilization by Output Feedback for a Class of Nonlinear Fractional‐Order Systems

Practical Stability for Conformable Time-Delay Systems

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