This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear d...This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear damping feedbacks. This paper shows that the system is well-posed and asymptotically stable by C0-semigroup theory. With some additional conditions, the spectrum of the system is shown to be located in a strip that is parallel to the imaginary axis and the set of all generalized eigenfunctions is completed in the state space. These lead to the conclusion that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis with parenthesis for the state space.展开更多
In this paper,we investigate the stabilization of an Euler-Bernoulli beam with time delays in the boundary controller.The boundary velocity feedback law is applied to obtain the closed-loop system.It is shown that thi...In this paper,we investigate the stabilization of an Euler-Bernoulli beam with time delays in the boundary controller.The boundary velocity feedback law is applied to obtain the closed-loop system.It is shown that this system generates a C_(0-)semigroup of linear operators.Moreover,the stability of the closed-loop system is discussed for different values of the controller constants and time delays via using spectral analysis and a suitable Lyapunov function.展开更多
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 opera...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.展开更多
基金This research is supported in part by the Natural Science Foundation of China under Grant No. 60874035 and by the Scientific Research Initiation Foundation of Civil Aviation University of China （08QD09X）.
文摘This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear damping feedbacks. This paper shows that the system is well-posed and asymptotically stable by C0-semigroup theory. With some additional conditions, the spectrum of the system is shown to be located in a strip that is parallel to the imaginary axis and the set of all generalized eigenfunctions is completed in the state space. These lead to the conclusion that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis with parenthesis for the state space.
文摘In this paper,we investigate the stabilization of an Euler-Bernoulli beam with time delays in the boundary controller.The boundary velocity feedback law is applied to obtain the closed-loop system.It is shown that this system generates a C_(0-)semigroup of linear operators.Moreover,the stability of the closed-loop system is discussed for different values of the controller constants and time delays via using spectral analysis and a suitable Lyapunov function.
基金supported in part by the National Natural Science Foundation of China(Grant No.61773277).
文摘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.
