一类有限变时滞微分系统的一致渐近稳定性研究
|
摘要
在实际问题中时滞会受到影响,随时间而变化,因此变时滞系统更具现实意义。根据泛函微分方程的稳定性理论,通过构造Lyapunov泛函,证明了一类有限变时滞微分系统零解的一致渐近稳定性。
The system will be affected by a variety of disturbances in practical problems, and the time delay will change with the development of time. Therefore, time-varying delay systems have more practical significance. Based on the stability theory of functional differential equations, the uniform asymptotic stability of zero solution of a class of differential systems with finite time-varying delays is proved by constructing the Lyapunov functions.
The system will be affected by a variety of disturbances in practical problems, and the time delay will change with the development of time. Therefore, time-varying delay systems have more practical significance. Based on the stability theory of functional differential equations, the uniform asymptotic stability of zero solution of a class of differential systems with finite time-varying delays is proved by constructing the Lyapunov functions.
引文
[1]郑祖庥.泛函微分方程[M].合肥:安徽教育出版社,1992:229-305.
[2]蒋威.退化,时滞微分系统[M].合肥:安徽大学出版社,1998:101-148.
[3]JACK K H,SJOERD M V L.Introduction to Functional Differential Equations[M].Berlin,New York:Springer-Verlag,1992:103-141.
[4]JIANG W.Eigenvalue and stability of singular differential delay systems[J].Mathematical Analysis And Applications,2004,297(1):305-316.
[5]方园,蒋威.一类含状态时滞线性退化系统的自适应控制[J].阜阳师范学院学报(自然科学版),2010,27(4):4-7.
[6]倪华,林发兴.关于有限时滞非线性微分方程零解的稳定性的两个结论[J].洛阳师范学院学报,2007,2:17-20.
[7]傅朝金,廖晓昕.时滞微分方程的稳定性[J].数学物理学报,2003,23A(4):494-498.
[8]柏艳,吴保卫,左宁.非线性变时滞系统的保性能鲁棒稳定性分析[J].纺织高校基础科学学报,2006,19(4):299-303.
[9]刘松.时滞微分系统的稳定性[D].合肥:安徽大学,2006.
[10]朱崇军.一类时滞微分方程的稳定性[J].衡阳师范学院学报(自然科学版),2002,23(3):46-48.
[11]肖淑肾.关于变系数线性方程的稳定性[J].系统科学与数学,1996,16(2):149-158.
[12]江明辉,沈轶,廖晓昕.变时滞随机微分方程的指数稳定性[J].工程数学学报,2006,23(6):961-965.
[13]梁松,吴然超.二解差分方程在不动点和周期点的稳定性[J].阜阳师范学院学报(自然科学版),2013,30(2):1-4.
[14]黄莹.泛函微分方程解的渐近性态[J].黑龙江大学自然科学学报,2006,23(4):427-429.
[15]葛莉,姚云飞.关于微分方程局部解存在定理证明的注记[J].阜阳师范学院学报(自然科学版),2013,30(1):77-80.
[16]TAN M C.Asymptotic stability of nonlinear system with unboundeddelays[J].Mathematical Analysis And Applications,2007,337(2):1010-1021.
[17]CARABALLO T,REAL J,SHAIKHET L.Method of Lyapunov functionals constructionin stability of delay evolution equations[J].Mathematical Analysis And Applications,2007,334(2):1130-1145.
[18]丁黎明,蒋威.一类含无界时滞微分系统的渐近稳定性[J].长春理工大学学报(自然科学版),2015,38(1):158-162.
[19]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,1999:40-60.
[20]黄琳.稳定性理论[M].北京:北京大学出版社,1992:173-186.
[2]蒋威.退化,时滞微分系统[M].合肥:安徽大学出版社,1998:101-148.
[3]JACK K H,SJOERD M V L.Introduction to Functional Differential Equations[M].Berlin,New York:Springer-Verlag,1992:103-141.
[4]JIANG W.Eigenvalue and stability of singular differential delay systems[J].Mathematical Analysis And Applications,2004,297(1):305-316.
[5]方园,蒋威.一类含状态时滞线性退化系统的自适应控制[J].阜阳师范学院学报(自然科学版),2010,27(4):4-7.
[6]倪华,林发兴.关于有限时滞非线性微分方程零解的稳定性的两个结论[J].洛阳师范学院学报,2007,2:17-20.
[7]傅朝金,廖晓昕.时滞微分方程的稳定性[J].数学物理学报,2003,23A(4):494-498.
[8]柏艳,吴保卫,左宁.非线性变时滞系统的保性能鲁棒稳定性分析[J].纺织高校基础科学学报,2006,19(4):299-303.
[9]刘松.时滞微分系统的稳定性[D].合肥:安徽大学,2006.
[10]朱崇军.一类时滞微分方程的稳定性[J].衡阳师范学院学报(自然科学版),2002,23(3):46-48.
[11]肖淑肾.关于变系数线性方程的稳定性[J].系统科学与数学,1996,16(2):149-158.
[12]江明辉,沈轶,廖晓昕.变时滞随机微分方程的指数稳定性[J].工程数学学报,2006,23(6):961-965.
[13]梁松,吴然超.二解差分方程在不动点和周期点的稳定性[J].阜阳师范学院学报(自然科学版),2013,30(2):1-4.
[14]黄莹.泛函微分方程解的渐近性态[J].黑龙江大学自然科学学报,2006,23(4):427-429.
[15]葛莉,姚云飞.关于微分方程局部解存在定理证明的注记[J].阜阳师范学院学报(自然科学版),2013,30(1):77-80.
[16]TAN M C.Asymptotic stability of nonlinear system with unboundeddelays[J].Mathematical Analysis And Applications,2007,337(2):1010-1021.
[17]CARABALLO T,REAL J,SHAIKHET L.Method of Lyapunov functionals constructionin stability of delay evolution equations[J].Mathematical Analysis And Applications,2007,334(2):1130-1145.
[18]丁黎明,蒋威.一类含无界时滞微分系统的渐近稳定性[J].长春理工大学学报(自然科学版),2015,38(1):158-162.
[19]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,1999:40-60.
[20]黄琳.稳定性理论[M].北京:北京大学出版社,1992:173-186.