scholarly journals An extension of estimation of domain of attraction for fractional order linear system subject to saturation control

2015 ◽  
Vol 47 ◽  
pp. 26-34 ◽  
Author(s):  
Esmat Sadat Alaviyan Shahri ◽  
Alireza Alfi ◽  
J.A. Tenreiro Machado
Keyword(s):  
Linear System ◽  
Fractional Order ◽  
Domain Of Attraction ◽  
Saturation Control ◽  
Order Linear

On the asymptotic stability of linear system of fractional-order difference equations

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Raghib Abu-Saris ◽  
Qasem Al-Mdallal
Keyword(s):  
Asymptotic Stability ◽  
Linear System ◽  
Fractional Order ◽  
Difference Equations ◽  
Equilibrium Solution ◽  
Initial Condition ◽  
System Of Difference Equations ◽  
Order Difference ◽  
Order Linear ◽  
The Stability

AbstractIn this paper we investigate the stability of the equilibrium solution of the νth order linear system of difference equations $(\Delta _{a + \nu - 1}^\nu y)(t) = \Lambda y(t + \nu - 1);t \in \mathbb{N}_a ,a \in \mathbb{R},and\Lambda \in \mathbb{R}^{p \times p} ,$ subject to the initial condition $y(a + \nu - 1) = y - 1,$, where 0 < ν < 1 and y−1 ∈ ℝp.

scholarly journals Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 200 ◽  
Author(s):  
Hong Li ◽  
Jun Cheng ◽  
Hou-Biao Li ◽  
Shou-Ming Zhong
Keyword(s):  
Stability Analysis ◽  
Linear System ◽  
Fractional Order ◽  
Stability Domain ◽  
Order System ◽  
Stability Conditions ◽  
Order Linear ◽  
Dynamic Matrix ◽  
Sufficient Stability ◽  
Sufficient Stability Conditions

In this paper, stability analysis of a fractional-order linear system described by the Caputo–Fabrizio (CF) derivative is studied. In order to solve the problem, character equation of the system is defined at first by using the Laplace transform. Then, some simple necessary and sufficient stability conditions and sufficient stability conditions are given which will be the basis of doing research of a fractional-order system with a CF derivative. In addition, the difference of stability domain between two linear systems described by two different fractional derivatives is also studied. Our results permit researchers to check the stability by judging the locations in the complex plane of the dynamic matrix eigenvalues of the state space.

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