A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.

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A high-gain observer with Mittag–Leffler rate of convergence for a class of nonlinear fractional-order systems

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2019.104909 ◽

2019 ◽

Vol 79 ◽

pp. 104909 ◽

Cited By ~ 3

Author(s):

O. Martínez-Fuentes ◽

R. Martínez-Guerra

Keyword(s):

Rate Of Convergence ◽

Fractional Order ◽

High Gain ◽

Fractional Order Systems ◽

High Gain Observer

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LAG SYNCHRONIZATION OF THE FRACTIONAL-ORDER SYSTEM VIA NONLINEAR OBSERVER

International Journal of Modern Physics B ◽

10.1142/s0217979211102253 ◽

2011 ◽

Vol 25 (29) ◽

pp. 3951-3964 ◽

Cited By ~ 10

Author(s):

HAO ZHU ◽

ZHONGSHI HE ◽

SHANGBO ZHOU

Keyword(s):

Numerical Simulation ◽

Fractional Order ◽

Stability Theorem ◽

Nonlinear Observer ◽

Order System ◽

Fractional Order Systems ◽

Lag Synchronization ◽

Systematic Method ◽

Fractional System ◽

The Stability

In this paper, based on the idea of nonlinear observer, lag synchronization of chaotic fractional system with commensurate and incommensurate order is studied by the stability theorem of linear fractional-order systems. The theoretical analysis of fractional-order systems in this paper is a systematic method. This technique is applied to achieve the lag synchronization of fractional-order Rössler's system, verified by numerical simulation.

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Output regulation of non-minimum phase nonlinear systems using an extended high-gain observer

2009 IEEE International Conference on Control and Automation ◽

10.1109/icca.2009.5410197 ◽

2009 ◽

Cited By ~ 4

Author(s):

Shahid Nazrulla ◽

Hassan K. Khalil

Keyword(s):

Nonlinear Systems ◽

High Gain ◽

Output Regulation ◽

Minimum Phase ◽

High Gain Observer

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Stability of Nonlinear Fractional-Order Time Varying Systems

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4031587 ◽

2015 ◽

Vol 11 (3) ◽

Cited By ~ 12

Author(s):

Sunhua Huang ◽

Runfan Zhang ◽

Diyi Chen

Keyword(s):

Laplace Transform ◽

Fractional Order ◽

Caputo Derivative ◽

Local Stability ◽

State Feedback ◽

Sufficient Condition ◽

Time Varying ◽

Fractional Order Systems ◽

Time Varying Systems ◽

The Stability

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order α : 0<α≤1 and 1<α<2 is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

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Event-triggered high-gain observer design for nonlinear systems

2016 35th Chinese Control Conference (CCC) ◽

10.1109/chicc.2016.7554513 ◽

2016 ◽

Cited By ~ 1

Author(s):

Yuan Huang ◽

Junzheng Wang ◽

Dawei Shi

Keyword(s):

Nonlinear Systems ◽

High Gain ◽

Observer Design ◽

High Gain Observer ◽

Event Triggered

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Analysis of Atangana–Baleanu fractional-order SEAIR epidemic model with optimal control

Advances in Difference Equations ◽

10.1186/s13662-021-03334-8 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Chernet Tuge Deressa ◽

Gemechis File Duressa

Keyword(s):

Numerical Simulation ◽

Optimal Control ◽

Fractional Order ◽

Control Strategy ◽

Epidemic Model ◽

Numerical Scheme ◽

Order Derivative ◽

Control Analysis ◽

Fractional Order Derivative ◽

Fractional Orders

AbstractWe consider a SEAIR epidemic model with Atangana–Baleanu fractional-order derivative. We approximate the solution of the model using the numerical scheme developed by Toufic and Atangana. The numerical simulation corresponding to several fractional orders shows that, as the fractional order reduces from 1, the spread of the endemic grows slower. Optimal control analysis and simulation show that the control strategy designed is operative in reducing the number of cases in different compartments. Moreover, simulating the optimal profile revealed that reducing the fractional-order from 1 leads to the need for quick starting of the application of the designed control strategy at the maximum possible level and maintaining it for the majority of the period of the pandemic.

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