Some problems of linear differential equations on abstract spaces and unbounded perturbations of linear operator semigroup  

作　　者：Genqi XU 

机构地区：[1]School of Mathematical Sciences,Tianjin University,Tianjin 300350,China

出　　处：《Frontiers of Mathematics in China》2022年第1期47-77,共31页中国高等学校学术文摘·数学（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Grant No.61773277).

摘　　要：This paper is a survey for development of linear distributed parameter system.At first we point out some questions existing in current study of control theory for the L^(p)linear system with an unbounded control operator and an unbounded observation operator,such as stabilization problem and observer theory that are closely relevant to state feedback operator.After then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup perturbations.As a principle,we propose a concept of admissible state feedback operator for system(A,B).Finally we give an existence result of admissible state feedback operators,including semigroup generation and the equivalent conditions of admissibility of state feedback operators,for an L^(p)well-posed system.

关 键 词：Linear differential equation semigroup perturbation Lp well-posed system admissible state feedback operator 

分 类 号：O152.7[理学—数学] O175[理学—基础数学]