Design of functional fractional-order observers for linear time-delay fractional-order systems in the time domain

2014 ◽  
Author(s):  
Y. Boukal ◽  
M. Darouach ◽  
M. Zasadzinski ◽  
N. E. Radhy
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Domain ◽  
Linear Time ◽  
Fractional Order Systems ◽  
The Time Domain

Geometrical design of fractional PDμ controllers for linear time-invariant fractional-order systems with time delay

2019 ◽  
Vol 233 (7) ◽  
pp. 815-829
Author(s):  
Adrián Josué Guel-Cortez ◽  
César-Fernando Méndez-Barrios ◽  
Emilio Jorge González-Galván ◽  
Gilberto Mejía-Rodríguez ◽  
Liliana Félix
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Linear Time ◽  
Simple Procedure ◽  
Geometric Approach ◽  
Fractional Order Systems ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant

This article presents a simple procedure that allows a practical design of fractional –[Formula: see text] controllers for single-input single-output linear time-invariant fractional-order systems subject to a constant time delay. The methodology is based on a geometric approach, which provides practical guidelines to design stabilizing and non-fragile PDμ controllers. The simplicity of the proposed approach is illustrated by considering several numerical examples encountered in the control literature. Moreover, with the aim of showing the performance of the PDμ over a classical PD controller, both controllers were implemented at the end of the article in an experimental test-bench consisting a teleoperated robotic system.

A Note on the Lyapunov Stability of Fractional-Order Nonlinear Systems

2017 ◽  
Author(s):  
Sara Dadras ◽  
Soodeh Dadras ◽  
Hadi Malek ◽  
YangQuan Chen
Keyword(s):  
Exponential Stability ◽  
Fractional Order ◽  
Lyapunov Stability ◽  
Time Domain ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
The Stability ◽  
The Time Domain

In this paper, stability of fractional order (FO) systems is investigated in the sense of the Lyapunov stability theory. A new definition for exponential stability of the fractional order systems is given and sufficient conditions are obtained for the exponential stability of the FO systems using the notion of Lyapunov stability. Besides, a less conservative sufficient condition is derived for asymptotical stability of FO systems. The stability analysis is done in the time domain. Numerical examples are given to show that the obtained conditions are effective and applicable in practice.

scholarly journals Finite-time stability of linear stochastic fractional-order systems with time delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lassaad Mchiri ◽  
Abdellatif Ben Makhlouf ◽  
Dumitru Baleanu ◽  
Mohamed Rhaima
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Finite Time ◽  
Stochastic Analysis ◽  
Fractional Order Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Analysis Techniques ◽  
Generalized Gronwall Inequality ◽  
Stability Of The Solution

AbstractThis paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for $\alpha \in (\frac{1}{2},1)$ α ∈ ( 1 2 , 1 ) . Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.

Practical stabilization of time-delay fractional-order systems by parametric controllers

2019 ◽  
Vol 95 ◽  
pp. 211-220 ◽  
Author(s):  
Narges Tahmasbi ◽  
Hojjat Ahsani Tehrani ◽  
Javad Esmaeili
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Practical Stabilization

Improving the time domain response of fractional order digital differentiators by windowing

2015 ◽  
Vol 107 ◽  
pp. 282-289 ◽  
Author(s):  
Chengyan Peng ◽  
Xiaochuan Ma ◽  
Geping Lin ◽  
Min Wang
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Time Domain Response ◽  
The Time Domain
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