Abstract
In this paper, we define a characteristic equation of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative. At the same time, by applying the Laplace transform and matrix theory we give a necessary and sufficient stability condition and some brief sufficient stability conditions. The proposed method is quite different from the other in the literature. In addition, we provide some examples to demonstrate the effectiveness of our results.
Highlights
Time delay is one of sources of instability and poor performance, so that dynamic systems with time delay have received extensive attention and research
There are different definitions of fractional derivatives [4], among which the most commonly used definition is the Caputo definition. It is called a smooth fractional derivative because it is suitable to be treated by the Laplace transform technique
Analysis of equations generated by different fractional derivatives has been done; see [5]
Summary
Time delay is one of sources of instability and poor performance, so that dynamic systems with time delay have received extensive attention and research. There are different definitions of fractional derivatives [4], among which the most commonly used definition is the Caputo definition. In the literature, it is called a smooth fractional derivative because it is suitable to be treated by the Laplace transform technique. Its advantages are mainly shown in the following aspects: First, it is less affected by the past; second, the asymptotic behavior of the new derivative, in contrast to the Caputo derivative, for the larger of the variable, is linearly increasing and diverging. In [13, 14] the kernel and no-index property of CF derivative separately are studied, which helps us to know more information on the derivative and its links to other fractional derivatives and real problems
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
