A Stability Analysis on Fractional Order Linear System with Nonlinear Saturated Disturbance

2015 ◽  
Vol 38 (5) ◽  
pp. 409-413 ◽  
Author(s):  
Esmat Sadat Alaviyan Shahri ◽  
Saeed Balochian
Keyword(s):  
Stability Analysis ◽  
Linear System ◽  
Fractional Order ◽  
Order Linear

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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