Long-term behavior of cross-dimensional linear dynamical systems
作者单位：ACCESS Linnaeus CenterSchool of Electrical Engineering KTH Royal Institute of Technology College of Automation Harbin Engineering University
会议名称：《第37届中国控制会议》
会议日期：2018年
学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 071101[理学-系统理论] 0701[理学-数学]
基 金：supported by Knut and Alice Wallenberg Foundation Swedish Foundation for Strategic Research Swedish Research Council
关 键 词：Long-term behavior cross-dimensional vector space cross-dimensional linear dynamical system dimension-boundedness basis Drazin inverse
摘 要：Let M and V denote the sets of finite-dimensional matrices and finite-dimensional column vectors,*** on the semitensor product and the vector addition,M and V both form a monoid,where V is *** addition,based on an equivalence relation on V,the induced quotient space V/ forms a vector *** this paper,we give a basis for the vector space V/,showing that V/ is of countably infinite *** addition,we give an explicit characterization for how the dimension of a vector in V changes caused by the repetitive actions of a matrix in M on the vector,and characterize the generalized inverse behavior of the repetitive actions.