分数阶线性退化微分系统有限时间镇定性问题

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

分数阶线性退化微分系统有限时间镇定性问题王盼盼, 张志信, 蒋威安徽大学数学科学学院, 合肥 230601 Finite-time Stabilizability of Fractional Linear Singular Differential System WANG Panpan, ZHANG Zhixin, JIANG WeiSchool of Mathematical Sciences, Anhui University, Hefei 230601

摘要
图/表
参考文献
相关文章(15)
点击分布统计
下载分布统计
-->

全文: PDF(299 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要本文通过构造新的Lyapunov函数，利用线性矩阵不等式（LMI）和广义Gronwall不等式，研究了分数阶线性退化微分系统的有限时间镇定性问题.充分考虑退化和扰动对系统稳定性的影响，给出了在状态反馈控制器作用下，分数阶退化微分系统在有限时间内镇定的充分条件.并通过两个例子验证了定理条件的可行性.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2019-01-16

PACS:

O175.15

基金资助:国家自然科学基金（11371027，11471015，11601003），安徽省自然科学基金（1608085MA12）和高等学校博士点专项科研资助基金（20123401120001）资助项目.

引用本文:

王盼盼, 张志信, 蒋威. 分数阶线性退化微分系统有限时间镇定性问题[J]. 应用数学学报, 2020, 43(1): 99-107. WANG Panpan, ZHANG Zhixin, JIANG Wei. Finite-time Stabilizability of Fractional Linear Singular Differential System. Acta Mathematicae Applicatae Sinica, 2020, 43(1): 99-107.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2020/V43/I1/99

[1]	Oldham K B, Spanier J. The fractional calculus. New York-London:Academic Press, 1974
[2]	Kilbas A, Srivastava H M, Trujillo J J. Theory and applications of fractional differential equations. New York:Elsevier, 2006
[3]	Feng J E, Wu Z, Sun J B. Finite-time control of linear singular systems with parametric uncertainties and disturbances. Acta Automatica Sinica, 2005, 31(4):634-637
[4]	Aguila-Camacho N, Duarte-Mermoud M A, Gallegos J A. Lyapunov functions for fractional order systems. Commun Nonlinear Sci. Numer. Simulat., 2014, 19:2951-2957
[5]	Ye H P, Gao J M, Din Y S. A generalized gronwall inequality and its application to a fractional differential equation. Math. Anal. Appl., 2014, 328:1075-1081
[6]	Zhao S W, Sun J T, Liu L. Finite-time stability of linear time-varying singular systems with impulsive effects. Int. J. Control, 2008, 81(11):1824-1829
[7]	Gallegos J A, Duarte-Mermoud M A. Boundedness and convergence on fractional order systems. Journal of Computational and Applied Mathematics, 2016, 296:815-826
[8]	Aguila-Camacho N, Duarte-Mermoud M A. Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems. ISA Transactions, 2016, 60:82-88
[9]	Zhang J F, Zhao X D, Chen Y. Finite-time stability and stabilization of fractional order positive switched systems. Circuits Syst Signal Process, 2016, 35:2450-2470
[10]	Gallegos J A, Duarte-Mermoud M A. On the Lyapunov theory for fractional order systems. Applied Mathematics and Computation, 2016, 287/288:161-170
[11]	Kamenkov G. On stability of motion over a finite interval of time. Appl. Mat. Mech, 1953, 17:529-540
[12]	Lazarević M P, Spasić A M. Finite time stability analysis of fractional order time delay systems:Gronwall's approach. Mathematical and Computer Modeling, 2009, 49:475-481
[13]	Lazarevic M P. Finite time stability analysis of PDα fractional control of robotic time-delay systems. Mechanics Research Communications, 2006, 33:269-279
[14]	Liu K W, Tu Z K. Finite time stabilization and boundedness of fractional differential neutral systems. College Mathematics, 2017, 33(4):24-31
[15]	Ma Y J, Wu B W, Wang Y E. Finite-time stability and finite-time boundedness of fractional order linear systems. Neurocomputing, 2016, 173:2076-2082
[16]	Li M M, Wang J R. Finite time stability of fractional delay differential equations. Applied Mathematics Letters, 2017, 64:170-176
[17]	Chen L P, Liu C, Wu R C, He Y G, Chai Y. Finite-time stability criteria for a class of fractional-order neural networks with delay. Neural Neural Comput Applic, 2016, 27:549-556
[18]	Jiang W. The constant variation formulae for singular fractional differential systems with delay. Computers and Mathematics with Applications, 2010, 59(3):1184-1190
[19]	Kunkel P, Mehrmann V. Differential algebraic equations. Switzerland:European Mathematical Society, 2006
[20]	Dai L. Singular control systems. Berlin, Heidelberg:Springer-Verlag, 1989
[21]	Campbell S L. Singular systems of differential equations. Sanfrancisco London Melbourne:Pitman advanced publishing Program, 1980
[22]	Campbell S L, Hong V, Linh V H. Stability criteria for differential-algebraic equations with multiple delays and their numerical solutions. Applied Mathematics and Computation, 2009, 208:397-415
[23]	Zhang Z X, Jiang W. Some results of the degenerate fractional differential system with delay. Computers and Mathematics with Applications, 2011, 62:1284-129
[24]	Pang D H, Jiang W. Finite-time stability analysis of fractional singular time-delay systems. Advances in Difference Equations, 2014, 259:1-11

[1]	杨礼昌, 蒋威, 盛家乐, 刘婷婷, Musarrt Nawaz. 一类具有多重时滞的分数阶中立型微分系统的相对可控性[J]. 应用数学学报, 2020, 43(1): 1-11.
[2]	刘有军, 赵环环, 康淑瑰. 分数阶微分方程组非振动解的存在性[J]. 应用数学学报, 2019, 42(5): 606-613.
[3]	叶专. Boussinesq方程的一个改进的Beale-Kato-Majda准则[J]. 应用数学学报, 2019, 42(4): 482-491.
[4]	杨晓忠, 邵京, 孙淑珍. 双项时间分数阶慢扩散方程的一类高效差分方法[J]. 应用数学学报, 2019, 42(4): 492-505.
[5]	樊明智, 王芬玲, 赵艳敏, 史艳华, 张亚东. 时间分数阶扩散方程双线性元的高精度分析[J]. 应用数学学报, 2019, 42(4): 535-549.
[6]	何道江, 盛玮芮, 方龙祥. 带有测量误差的Wiener退化模型的客观Bayes分析[J]. 应用数学学报, 2019, 42(4): 506-517.
[7]	任金城, 石东洋. 分布阶波方程全离散有限元方法的高精度分析新途径[J]. 应用数学学报, 2019, 42(3): 410-424.
[8]	董佳华, 冯育强, 蒋君. 非线性隐式分数阶微分方程耦合系统初值问题[J]. 应用数学学报, 2019, 42(3): 356-370.
[9]	冯立杰. 具有分数阶导数的积分边值问题正解的存在性[J]. 应用数学学报, 2019, 42(2): 254-265.
[10]	阎晓妹, 尚婷, 赵小国. 基于分数阶滑模控制器的不确定分数阶混沌系统同步[J]. 应用数学学报, 2018, 41(6): 765-776.
[11]	田元生, 李小平, 葛渭高. p-Laplacian分数阶微分方程边值问题正解的存在性[J]. 应用数学学报, 2018, 41(4): 529-539.
[12]	李志广, 康淑瑰. 一类退化抛物变分不等式问题解的存在性和唯一性[J]. 应用数学学报, 2018, 41(3): 289-304.
[13]	王虎, 田晶磊, 孙玉琴, 于永光. 具有阶段结构的时滞分数阶捕食者-食饵系统的稳定性分析[J]. 应用数学学报, 2018, 41(1): 27-42.
[14]	张文彪, 易鸣. 一类抽象非线性分数阶微分方程的Cauchy问题[J]. 应用数学学报, 2017, 40(6): 874-882.
[15]	王亚平, 刘立山, 吴永洪. 有Riemann-Stieltjes积分边界条件的非线性奇异分数阶微分方程边值问题正解的存在性[J]. 应用数学学报, 2017, 40(5): 752-769.

PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14714