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

Hong Li, Jun Cheng, Hou-Biao Li and Shou-Ming Zhong
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Hong Li: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Jun Cheng: College of Automation and Electronic Engineering, Qingdao Universtiy of Science and Technology, Qingdao 266061, China
Hou-Biao Li: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Shou-Ming Zhong: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Mathematics, 2019, vol. 7, issue 2, 1-9

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.

Keywords: fractional model; stability; Caputo–Fabrizio derivative; Caputo fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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