|本期目录/Table of Contents|

 一种迟滞微分系统的稳定与控制问题研究(PDF)

《内蒙古大学学报(自然科学版)》[ISSN:1000-9035/CN:22-1262/O4]

期数:
2017年01期
页码:
23-29
栏目:
研究论文
出版日期:
2017-01-15

文章信息/Info

Title:
 Research on the Problem of the Stability and Control of a Kind of Delay Differential System
作者:
 伊丽娜包俊东套格图桑
 内蒙古师范大学数学科学学院,呼和浩特 010022
Author(s):
 YI Li-naBAO Jun-dongTaogetusang
 College of Mathematical Science,Inner Mongolia Normal University,Hohhot 010022,China
关键词:
 一种迟滞微分系统双曲函数型辅助方程精确解稳定与控制
Keywords:
 a kind of delay differential systemhyperbolic function type auxiliary equationaccurate solutionstability and control
分类号:
-
DOI:
-
文献标识码:
A
摘要:
 基于李雅普诺夫两种方法,给出一种双曲函数型辅助方程及其相关结论;通过几个步骤,研究了一种迟滞微分系统的求解、稳定与控制问题.步骤一、给出双函数型辅助方程的精确解.步骤二、通过双曲函数变换与双曲函数型辅助方程,将一种迟滞微分系统的求解问题转化为非线性代数方程组的求解问题.步骤三、借助符号计算系统Mathematica求出代数方程组的解,并构造了一种迟滞微分系统的精确解.步骤四、用符号计算系统Mathematica研究迟滞微分系统的稳定与控制问题.
Abstract:
 Two kinds of Lyapunov method are presented to put forward a kind of hyperbolic function type auxiliary equation and its relative conclusions.By some steps,the problems of solving the solution,stability and control of a kind of delay differential system are researched.Step 1,the accurate solutions of the hyperbolic function type auxiliary equation are presented.Step 2,by a hyperbolic function transformation and hyperbolic function type auxiliary equation,the problem of solving solutions of a kind of delay differential system is changed to the problem of solving solutions of the nonlinear algebra equations.Step 3,with the help of the symbol calculate system Mathematica,the solutions of the algebra equations are solved,and the accurate solutions of a kind of delay differential system are constructed.Step 4,with the help of the symbol calculate system Mathematica,the problem of the stability and control of a kind of delay differential system is researched.

参考文献/References

 [1] 廖晓昕.稳定性的理论、方法和应用[M].武汉:华中科技大学出版社,2009.
[2] 王高雄,周之铭,朱思铭,王寿松.常微分方程[M].第3版.北京:高等教育出版社,2006.
[3] 孔庆凯.非线性系统稳定性及其在力学系统中的应用[D].成都:四川大学,2001.
[4] 庄万.常微分方程习题解[M].济南:山东科学技术出版社,2003.
[5] 李德生,张鸿庆.非线性演化方程椭圆函数解的一种简单求法及其应用[J].物理学报,2006,55(4):1565-1570.
[6] Fu Z T,Liu S K,Liu S D.A new approach to solve nonlinear wave equations[J].Commun Theore Phys(Beijing,China),2003,39(1):27-30.
[7] Yang J R,Mao J J.Complexiton solutions of a special coupled mKdV system[J].Chin Phys Lett,2008,25(5):1527-1530.
[8] 余丽琴,田立新.Degasperis-Procesi方程的孤立尖波解[J].数学的实践与认识,2006,36(3):261-266.
[9] Chen Y,Li B,Zhang H Q.Generalized Riccati equation expansion method and its application to the Bogoyavlenskiis generalized breaking soliton equation[J].Chin Phys,2003,12(9):940-945.
[10] Khaled A Gepreel,Saleh Omran.Exact solutions for nonlinear partial fractional differential equations[J].Chin Phys B,2012,21(11):110204(1-7).
[11] 套格图桑.辅助方程构造CH-r方程的无穷序列尖峰孤立波解[J].工程数学学报,2012,29(6):865-876.
[12] 马正义,马松华,杨毅.具有色散系数的(2+1)维非线性Schrdinger方程的有理解和空间孤子[J].物理学报,2012,61(19):190508(1-5).
[13] 王军民.修正的Korteweg de Vries-正弦Gordon方程的Riemannθ函数解[J].物理学报,2012,61(8):080201(1-5).
[14] 张卫国,常谦顺,李用声.具任意次非线性项的Liénard方程的精确解及其应用[J].数学物理学报,2005,25A(1):119-129.
[15] 刘萍.若干耦合非线性系统的严格解研究[D].上海:上海交通大学,2008.
[16] 套格图桑.一般格子方程新的无穷序列精确解[J].物理学报,2010,59(10):6711-6717.
[17] Taogetusang,Sirendaoerji,Li S M.New application to Riccati equation[J].Chin Phys B,2010,19(8):080303(1-8).

备注/Memo

备注/Memo:
 收稿日期:2016-09-08
基金项目:国家自然科学基金(11361040);内蒙古自治区自然科学基金(2015MS0128);内蒙古自治区高等学校科学研究基金(NJZY16180);内蒙古自治区2016年硕士研究生科研创新项目(S20161013502);内蒙古师范大学研究生科研创新基金项目(CXJJS16081)
作者简介:伊丽娜(1991-),女(蒙古族),内蒙古通辽人,2015级硕士研究生.研究方向:复杂系统的稳定与控制.E-mail:573028703@qq.com
更新日期/Last Update: