Full Text:   <3321>

Summary:  <1336>

CLC number: O231

On-line Access: 2021-10-08

Received: 2020-08-30

Revision Accepted: 2020-11-29

Crosschecked: 2021-08-06

Cited: 0

Clicked: 5222

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Zahra Sadat Aghayan

https://orcid.org/0000-0002-8488-3685

Alireza Alfi

https://orcid.org/0000-0002-7034-0735

J. A. Tenreiro Machado

https://orcid.org/0000-0003-4274-4879

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2021 Vol.22 No.10 P.1402-1412

http://doi.org/10.1631/FITEE.2000438


Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation


Author(s):  Zahra Sadat Aghayan, Alireza Alfi, J. A. Tenreiro Machado

Affiliation(s):  Faculty of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood 36199-95161, Iran; more

Corresponding email(s):   a_alfi@shahroodut.ac.ir

Key Words:  Fractional-order system, Stability, Neutral delay, Robust, Saturation


Share this article to: More <<< Previous Article|

Zahra Sadat Aghayan, Alireza Alfi, J. A. Tenreiro Machado. Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(10): 1402-1412.

@article{title="Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation",
author="Zahra Sadat Aghayan, Alireza Alfi, J. A. Tenreiro Machado",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="22",
number="10",
pages="1402-1412",
year="2021",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.2000438"
}

%0 Journal Article
%T Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation
%A Zahra Sadat Aghayan
%A Alireza Alfi
%A J. A. Tenreiro Machado
%J Frontiers of Information Technology & Electronic Engineering
%V 22
%N 10
%P 1402-1412
%@ 2095-9184
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2000438

TY - JOUR
T1 - Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation
A1 - Zahra Sadat Aghayan
A1 - Alireza Alfi
A1 - J. A. Tenreiro Machado
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 22
IS - 10
SP - 1402
EP - 1412
%@ 2095-9184
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2000438


Abstract: 
This study analyzes the problem of robust stability of fractional-order delay systems of neutral type under actuator saturation. A Lyapunov–Krasovskii (LK) function is constructed and conditions of the asymptotic robust stability of such systems are given, which are formulated by linear matrix inequalities (LMIs), using the Lyapunov direct method. An algorithm is introduced to compute the gain of the state feedback controller for extending the domain of attraction. The theoretical results are validated using some numerical examples.

执行器饱和条件下不确定的中立型分数阶时滞系统的稳定性分析

Zahra Sadat AGHAYAN1,Alireza ALFI1,J. A. TENREIRO MACHADO2
1沙鲁德科技大学电气与机器人工程系,伊朗沙德鲁市,36199-95161
2波尔图理工学院工程研究所,葡萄牙波尔图市,4249-015
摘要:分析了执行器饱和条件下中立型分数阶时滞系统的鲁棒稳定性问题。构建了一个Lyapunov-Krasovskii(LK)函数,并给出此类系统的渐近鲁棒稳定性条件,这些条件使用Lyapunov直接方法构造的线性矩阵不等式(LMIs)表示。引入一种算法计算状态反馈控制器的增益以扩展吸引域。数值示例验证了理论结果。

关键词:分数阶系统;稳定性;中立时滞;鲁棒性;饱和性

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Aghayan ZS, Alfi A, Tenreiro Machado JA, 2020. Stability analysis of fractional order neutral-type systems considering time varying delays, nonlinear perturbations, and input saturation. Math Methods Appl Sci, 43(17):10332-10345.

[2]Alaviyan Shahri ES, Alfi A, Tenreiro Machado JA, 2018a. Robust stability and stabilization of uncertain fractional order systems subject to input saturation. J Vibr Contr, 24(16):3676-3683.

[3]Alaviyan Shahri ES, Alfi A, Tenreiro Machado J, 2018b. Stability analysis of a class of nonlinear fractional-order systems under control input saturation. Int J Robust Nonl Contr, 28(7):2887-2905.

[4]Altun Y, Tunç C, 2019. On exponential stability of solutions of nonlinear neutral differential systems with discrete and distributed variable lags. Nonl Stud, 26(2):455-466.

[5]Badri P, Sojoodi M, 2019a. LMI-based robust stability and stabilization analysis of fractional-order interval systems with time-varying delay. https://arxiv.org/abs/1909.08415v1

[6]Badri P, Sojoodi M, 2019b. Robust stabilisation of fractional-order interval systems via dynamic output feedback: an LMI approach. Int J Syst Sci, 50(9):1718-1730.

[7]Badri P, Sojoodi M, 2019c. Stability and stabilization of fractional-order systems with different derivative orders: an LMI approach. Asian J Contr, 21(5):2270-2279.

[8]Baleanu D, Jajarmi A, Asad JH, 2019a. Classical and fractional aspects of two coupled pendulums. Roman Rep Phys, 71(1):103.

[9]Baleanu D, Sajjadi SS, Jajarmi A, et al., 2019b. New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator. Eur Phys J Plus, 134(4):181.

[10]Barbarossa M, Hadeler K, Kuttler C, 2014. State-dependent neutral delay equations from population dynamics. J Math Biol, 69(4):1027-1056.

[11]Binazadeh T, Yousefi M, 2018. Asymptotic stabilization of a class of uncertain nonlinear time-delay fractional-order systems via a robust delay-independent controller. J Vibr Contr, 24(19):4541-4550.

[12]Chartbupapan W, Bagdasar O, Mukdasai K, 2020. A novel delay-dependent asymptotic stability conditions for differential and Riemann–Liouville fractional differential neutral systems with constant delays and nonlinear perturbation. Mathematics, 8(1):82.

[13]Chen WS, Dai H, Song YF, et al., 2017. Convex Lyapunov functions for stability analysis of fractional order systems. IET Contr Theory Appl, 11(7):1070-1074.

[14]Dubey VP, Kumar R, Kumar D, et al., 2020. An efficient computational scheme for nonlinear time fractional systems of partial differential equations arising in physical sciences. Adv Differ Equat, 2020(1):46.

[15]Elahi A, Alfi A, 2017. Finite-time H control of uncertain networked control systems with randomly varying communication delays. ISA Trans, 69:65-88.

[16]El Fezazi N, El Haoussi F, Tissir EH, et al., 2017. Robust stabilization using LMI techniques of neutral time-delay systems subject to input saturation. J Phys Conf Ser, 783(1):012031.

[17]Gu KQ, Kharitonov VL, Chen J, 2003. Stability of Time-Delay Systems. Birkhäuser, Boston, USA.

[18]Han QL, 2005. Stability analysis for a partial element equivalent circuit (PEEC) model of neutral type. Int J Circ Theory Appl, 33(4):321-332.

[19]He BB, Zhou HC, Kou CH, 2020. Controllability of fractional-order damped systems with time-varying delays in control. Front Inform Technol Electron Eng, 21(6):844-855.

[20]Hu BX, Song QK, Zhao ZJ, 2020. Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertainties: LMI approach. Appl Math Comput, 373:125033.

[21]Hu TT, He Z, Zhang XJ, et al., 2020. Finite-time stability for fractional-order complex-valued neural networks with time delay. Appl Math Comput, 365:124715.

[22]Kilbas AA, Bonilla B, Trukhillo K, 2000. Fractional integrals and derivatives and differential equations of fractional order in weighted spaces of continuous functions. Dokl Nats Akad Nauk Belar, 44(6):18-22.

[23]Kilbas AA, Srivastava HM, Trujillo JJ, 2006. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, the Netherlands.

[24]Li JD, Wu ZB, Huang NJ, 2019. Asymptotical stability of Riemann–Liouville fractional-order neutral-type delayed projective neural networks. Neur Process Lett, 50(1):565-579.

[25]Lien CH, Yu KW, Lin YF, et al., 2008. Global exponential stability for uncertain delayed neural networks of neutral type with mixed time delays. IEEE Trans Syst Man Cybern Part B (Cybern), 38(3):709-720.

[26]Liu MY, Dassios I, Milano F, 2019. On the stability analysis of systems of neutral delay differential equations. Circ Syst Signal Process, 38(4):1639-1653.

[27]Liu S, Jiang W, Li XY, et al., 2016. Lyapunov stability analysis of fractional nonlinear systems. Appl Math Lett, 51:13-19.

[28]Manitius A, 1984. Feedback controllers for a wind tunnel model involving a delay: analytical design and numerical simulation. IEEE Trans Autom Contr, 29(12):1058-1068.

[29]Mohsenipour R, Fathi Jegarkandi M, 2019. Robust stability analysis of fractional-order interval systems with multiple time delays. Int J Robust Nonl Contr, 29(6):1823-1839.

[30]Pahnehkolaei SMA, Alfi A, Machado JAT, 2017a. Chaos suppression in fractional systems using adaptive fractional state feedback control. Chaos Sol Fract, 103:488-503.

[31]Pahnehkolaei SMA, Alfi A, Machado JAT, 2017b. Uniform stability of fractional order leaky integrator echo state neural network with multiple time delays. Inform Sci, 418-419:703-716.

[32]Pahnehkolaei SMA, Alfi A, Machado JAT, 2019a. Delay-dependent stability analysis of the QUAD vector field fractional order quaternion-valued memristive uncertain neutral type leaky integrator echo state neural networks. Neur Netw, 117:307-327.

[33]Pahnehkolaei SMA, Alfi A, Machado JAT, 2019b. Stability analysis of fractional quaternion-valued leaky integrator echo state neural networks with multiple time-varying delays. Neurocomputing, 331:388-402.

[34]Petersen IR, 1987. A stabilization algorithm for a class of uncertain linear systems. Syst Contr Lett, 8(4):351-357.

[35]Pu YF, Wang J, 2020. Fractional-order global optimal backpropagation machine trained by an improved fractional-order steepest descent method. Front Inform Technol Electron Eng, 21(6):809-833.

[36]Ren HL, Zong GD, Hou LL, et al., 2017. Finite-time resilient decentralized control for interconnected impulsive switched systems with neutral delay. ISA Trans, 67:19-29.

[37]Shahri ESA, Alfi A, Machado JAT, 2015. An extension of estimation of domain of attraction for fractional order linear system subject to saturation control. Appl Math Lett, 47:26-34.

[38]Shahri ESA, Alfi A, Tenreiro Machado JA, 2017. Stabilization of fractional-order systems subject to saturation element using fractional dynamic output feedback sliding mode control. J Comput Nonl Dynam, 12(3):031014.

[39]Shahri ESA, Alfi A, Machado JAT, 2020. Lyapunov method for the stability analysis of uncertain fractional-order systems under input saturation. Appl Math Model, 81:663-672.

[40]Song S, Park JH, Zhang BY, et al., 2020. Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation. Appl Math Comput, 364:124662.

[41]Udhayakumar K, Rakkiyappan R, Cao JD, et al., 2020. Mittag–Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks. Front Inform Technol Electron Eng, 21(2):234-246.

[42]Valério D, Trujillo JJ, Rivero M, et al., 2013. Fractional calculus: a survey of useful formulas. Eur Phys J Spec Top, 222(8):1827-1846.

[43]Witrant E, 2005. Stabilisation des Syst‘emes Commandés par Réseaux (Stability of Networked Control Systems). PhD Thesis, Institut National Polytechnique, Grenoble, France (in French).

[44]Yang HY, Yang YZ, Han FJ, et al., 2019. Containment control of heterogeneous fractional-order multi-agent systems. J Franklin Inst, 356(2):752-765.

[45]Zhang FZ, 2006. The Schur Complement and Its Applications. Springer Science & Business Media, Boston, USA.

[46]Zhang S, Liu L, Cui XS, 2019. Robust FOPID controller design for fractional-order delay systems using positive stability region analysis. Int J Robust Nonl Contr, 29(15):5195-5212.

[47]Zhang XF, Chen YQ, 2018. Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: the 0<α<1 case. ISA Trans, 82:42-50.

[48]Zhang Y, Sun HG, Stowell HH, et al., 2017. A review of applications of fractional calculus in Earth system dynamics. Chaos Sol Fract, 102:29-46.

[49]Zhu CH, Li XD, Wang KN, 2020. An anti-windup approach for nonlinear impulsive system subject to actuator saturation. Chaos Sol Fract, 133:109658.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE