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

作     者：Genqi XU Genqi XU

作者机构：School of Mathematical SciencesTianjin UniversityTianjin 300350China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2022年第17卷第1期

页      面：47-77页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：Linear differential equation semigroup perturbation Lp well-posed system admissible state feedback operator 

摘      要：This paper is a survey for development of linear distributed parameter *** 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 *** then we survey briefly some results on relevant problems that are related to solvability of linear differential equations in general Banach space and semigroup *** 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.