Stability of a dynamical system may change from stable to unstable or vice versa, with the change of some parameter of the system. This is the phenomenon of stability switches, and it has been investigated intensively in the literature for conventional time-delay systems. This paper studies the stability switches of a class of fractional-delay systems whose coefficients depend on the time delay. Two simple formulas in closed-form have been established for determining the crossing direction of the characteristic roots at a given critical point, which is one of the two key steps in the analysis of stability switches. The formulas are expressed in terms of the Jacobian determinant of two auxiliary real-valued functions that are derived directly from the characteristic function, and thus, can be easily implemented. Two examples are given to illustrate the main results and to show an important difference between the fractional-delay systems with delay-dependent coefficients and the ones with delay-free coefficients from the viewpoint of stability switches.
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November 2018
Research-Article
Stability Switches of a Class of Fractional-Delay Systems With Delay-Dependent Coefficients
Xinghu Teng,
Xinghu Teng
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China;
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China;
Department of Basic Courses,
PLA Army Engineering University,
Nanjing 211101, China
PLA Army Engineering University,
Nanjing 211101, China
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Zaihua Wang
Zaihua Wang
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: zhwang@nuaa.edu.cn
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: zhwang@nuaa.edu.cn
Search for other works by this author on:
Xinghu Teng
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China;
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China;
Department of Basic Courses,
PLA Army Engineering University,
Nanjing 211101, China
PLA Army Engineering University,
Nanjing 211101, China
Zaihua Wang
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: zhwang@nuaa.edu.cn
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: zhwang@nuaa.edu.cn
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 10, 2017; final manuscript received July 31, 2018; published online September 10, 2018. Assoc. Editor: Dumitru Baleanu.
J. Comput. Nonlinear Dynam. Nov 2018, 13(11): 111005 (9 pages)
Published Online: September 10, 2018
Article history
Received:
November 10, 2017
Revised:
July 31, 2018
Citation
Teng, X., and Wang, Z. (September 10, 2018). "Stability Switches of a Class of Fractional-Delay Systems With Delay-Dependent Coefficients." ASME. J. Comput. Nonlinear Dynam. November 2018; 13(11): 111005. https://doi.org/10.1115/1.4041083
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