摘要
讨论了具有多种时滞的分数阶微分方程的相对可控性问题.提出了一类具有多种时滞的分数阶微分系统,得到了系统方程的解.利用Gramian矩阵证明了系统的相对可控性,提出并建立了具有多种时滞的分数阶系统的相对可控性的充分必要条件.运用Schauder不动点定理、压缩映像原理、Arzela-Ascoli定理得到非线性系统的解,证明了非线性系统具有相对可控性.通过实例验证了所得理论的正确性.
A class of fractional order differential systems with multiple time delays is proposed,and then the solution of the system equation is obtained through the knowledge of fractional order differential equations and delay differential equations.Gramian matrix is used to prove whether the system has relative controllability.The necessary and sufficient conditions for relative controllability of fractional order system with multiple time delays are proposed and established.The solution of nonlinear system is obtained by using Schauder fixed point theorem,compressed image principle and Arzela-Ascoli theorem.It is proved that the nonlinear system has relative controllability.The correctness of this theory is tested by a series of examples.
作者
王寻
高瑞梅
刘俊鹏
WANG Xun;GAO Rui-mei;LIU Jun-peng(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130022,China)
出处
《东北师大学报（自然科学版）》
CAS
北大核心
2023年第2期45-51,共7页
Journal of Northeast Normal University(Natural Science Edition)
基金
吉林省自然科学基金资助项目(20180101229JC)。
关键词
相对可控性
时滞
微分方程
动力系统
relative controllability
delay
differential equation
dynamical system
