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Research Papers

On the Stability of Fractional-Order Systems of Neutral Type

[+] Author and Article Information
Mohammad Ali Pakzad

Department of Electrical Engineering,
Science and Research Branch,
Islamic Azad University,
Tehran 14778-93855, Iran
e-mail: m.pakzad@srbiau.ac.ir

Sara Pakzad

Department of Electrical Engineering,
South Tehran Branch,
Islamic Azad University,
Tehran 14778-93855, Iran
e-mail: spakzad@pedc.ir

Mohammad Ali Nekoui

Faculty of Electrical and Computer Engineering,
K. N. Toosi University of Technology,
Seyed-Khandan, P. O. Box 16315-1355,
Tehran, Iran
e-mail: manekoui@eetd.kntu.ac.ir

For interpretation of the references to color in figures 3 and 4, the reader is referred to the web version of this article

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 21, 2014; final manuscript received April 28, 2014; published online April 6, 2015. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 10(5), 051013 (Sep 01, 2015) (7 pages) Paper No: CND-14-1079; doi: 10.1115/1.4027593 History: Received March 21, 2014; Revised April 28, 2014; Online April 06, 2015

The aim of this study is to offer a new analytical method for the stability testing of neutral type linear time-invariant (LTI) time-delayed fractional-order systems with commensurate orders and multiple commensurate delays. It is evident from the literature that the stability assessment of this class of dynamics remains unsolved yet and this is the first attempt to take up this challenging problem. The method starts with the determination of all possible purely imaginary characteristic roots for any positive time delay. To achieve this, the Rekasius transformation is used for the transcendental terms in the characteristic equation. An explicit analytical expression in terms of the system parameters which reveals the stability regions (pockets) in the domain of time delay has been presented. The number of unstable roots in each delay interval is calculated with the definition of root tendency (RT) on the boundary of each interval. Two example case studies are also provided, which are not possible to analyze using any other methodology known to the authors.

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Topics: Stability , Delays
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References

Pakzad, M. A., and Pakzad, S., 2012, “Stability Map of Fractional Order Time-Delay Systems,” WSEAS Trans. Syst., 10(11), pp. 541–550.
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Pakzad, M. A., 2012, “Kalman Filter Design for Time Delay Systems,” WSEAS Trans. Syst., 11(10), pp. 551–560.
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Figures

Grahic Jump Location
Fig. 1

Root-locus for C1(s, τ) from τ = 0.4 until τ = 2.4

Grahic Jump Location
Fig. 2

The natural responses of system (32) for different values of the delay

Grahic Jump Location
Fig. 3

Root-locus for C2(s, τ) from τ = 0.1 until τ = 2.4

Grahic Jump Location
Fig. 4

Root-locus for C2(s, τ) from τ = 0.1 until τ = 3.5

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