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Mathematics 2019, 7(2), 200; https://doi.org/10.3390/math7020200

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

1
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2
College of Automation and Electronic Engineering, Qingdao Universtiy of Science and Technology, Qingdao 266061, China
*
Author to whom correspondence should be addressed.
Received: 31 December 2018 / Revised: 13 February 2019 / Accepted: 15 February 2019 / Published: 20 February 2019
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Abstract

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. View Full-Text
Keywords: fractional model; stability; Caputo–Fabrizio derivative; Caputo fractional derivative fractional model; stability; Caputo–Fabrizio derivative; Caputo fractional derivative
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Li, H.; Cheng, J.; Li, H.-B.; Zhong, S.-M. Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative. Mathematics 2019, 7, 200.

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