Stability Analysis and Stabilization of Fractional-Order Systems With Distributed Delay

被引：1

作者：

Chen, Yi-Nan ^{[1
,2
]}

Lu, Jun-Guo ^{[1
,2
]}

Zhu, Zhen ^{[1
,2
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Automat, Shanghai, Peoples R China

[2] Minist Educ China, Key Lab Syst Control & Informat Proc, Shanghai, Peoples R China

来源：

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL | 2025年 / 35卷 / 05期

基金：

中国国家自然科学基金;

关键词：

distributed delay; fractional-order; robust stability; stability; stabilization;

D O I：

10.1002/rnc.7750

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper investigates the stability and stabilization problems of fractional-order systems with distributed delays (FOSDDs). Firstly, with the frequency sweeping technique and generalized Kalman-Yakubovic-Popov (KYP) lemma, a novel stability condition for FOSDDs is proposed. Secondly, based on the proposed stability condition, a robust stability condition for the uncertain FOSDDs with norm-bounded uncertainties is derived. Thirdly, based on the proposed robust stability condition, a novel stabilization condition for the uncertain FOSDDs with norm-bounded uncertainties is obtained. Finally, several numerical examples are provided to show the effectiveness of the proposed results. Moreover, in the numerical examples, the comparison of the proposed results with the existing results for FOSDDs is shown to demonstrate that the obtained results are less conservative.

引用

页码：1705 / 1718

页数：14

共 37 条

[1]

Baleanu D, 2011, ROM J PHYS, V56, P636

[2] Leader-Follower Weighted Consensus of Nonlinear Fractional-Order Multiagent Systems Using Current and Time Delay State Information [J].

Chen, Liping ;

Liu, Chuang ;

Chu, Zhaobi ;

Lopes, Antonio M. ;

Chen, Yangquan .

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS, 2024, 54 (09) :5814-5823

[3] A Comparison Study of Time-Domain Computation Methods for Piecewise Smooth Fractional-Order Circuit Systems [J].

Chen, Xi ;

Zheng, Feng ;

Wei, Yewen .

FRACTAL AND FRACTIONAL, 2023, 7 (03)

[4] Order-Dependent Stability and Stabilization Conditions for Fractional-Order Systems With Distributed Delays [J].

Chen, Yi-Nan ;

Lu, Jun-Guo ;

Jin, Xiao-Chuang ;

Zhu, Zhen .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2024, 71 (03) :1301-1305

[5] Pseudo-state feedback stabilization of commensurate fractional order systems [J].

Farges, Christophe ;

Moze, Mathieu ;

Sabatier, Jocelyn .

AUTOMATICA, 2010, 46 (10) :1730-1734

[6] Circuit Realization of the Fractional-Order Sprott K Chaotic System with Standard Components [J].

Gokyildirim, Abdullah .

FRACTAL AND FRACTIONAL, 2023, 7 (06)

[7] An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers [J].

Hamamci, Serdar Ethem .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2007, 52 (10) :1964-1969

[8] Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems [J].

Hamamci, Serdar Ethem ;

Koksal, Muhammet .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (05) :1621-1629

[9] Generalized LFT-based representation of parametric uncertain models [J].

Hecker, S ;

Varga, A .

EUROPEAN JOURNAL OF CONTROL, 2004, 10 (04) :326-337

[10] The stability and control of fractional nonlinear system with distributed time delay [J].

Hu, Jian-Bing ;

Zhao, Ling-Dong ;

Lu, Guo-Ping ;

Zhang, Shi-Bing .

APPLIED MATHEMATICAL MODELLING, 2016, 40 (04) :3257-3263

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