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Siu Pang Yung - One of the best experts on this subject based on the ideXlab platform.

  • RIESZ BASIS PROPERTY OF TIMOSHENKO BEAMS WITH BOUNDARY FEEDBACK CONTROL
    International Journal of Mathematics and Mathematical Sciences, 2020
    Co-Authors: De-xing Feng, Genqi Xu, Siu Pang Yung
    Abstract:

    A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert Spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the State Hilbert Space.

  • Exponential stability of variable coefficients Rayleigh beams under boundary feedback controls: A Riesz basis approach
    Systems & Control Letters, 2020
    Co-Authors: Jun-min Wang, Genqi Xu, Siu Pang Yung
    Abstract:

    In this paper, we study the boundary stabilizing feedback control problem of Rayleigh beams that have non-homogeneous spatial parameters. We show that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, stiffness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen. The main steps are a detail asymptotic analysis of the spectrum of the system and the proving of that the generalized eigenfunctions of the feedback control system form a Riesz basis in the State Hilbert Space. As a by-product, a conjecture in Guo (J. Optim. Theory Appl. 112(3) (2002) 529) is answered.

  • Stabilization of wave systems with input delay in the boundary control
    ESAIM: Control Optimisation and Calculus of Variations, 2006
    Co-Authors: Genqi Xu, Siu Pang Yung, Leong Kwan Li
    Abstract:

    In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight (1 � µ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the State Hilbert Space. Furthermore, we show that when the weight µ> 1 , for any time delay, we can choose a suitable feedback gain so that the closed loop system is exponentially stable. When µ = 1 ,w e show that the system is at most asymptotically stable. When µ< 1 , the system is always unstable.

  • Exponential Stabilization of Laminated Beams with Structural Damping and Boundary Feedback Controls
    Siam Journal on Control and Optimization, 2005
    Co-Authors: Jun-min Wang, Genqi Xu, Siu Pang Yung
    Abstract:

    We study the boundary stabilization of laminated beams with structural damping which describes the slip occurring at the interface of two-layered objects. By using an invertible matrix function with an eigenvalue parameter and an asymptotic technique for the first order matrix differential equation, we find out an explicit asymptotic formula for the matrix fundamental solutions and then carry out the asymptotic analyses for the eigenpairs. Furthermore, we prove that there is a sequence of generalized eigenfunctions that forms a Riesz basis in the State Hilbert Space, and hence the spectrum determined growth condition holds. Furthermore, exponential stability of the closed-loop system can be deduced from the eigenvalue expressions. In particular, the semigroup generated by the system operator is a $C_0$-group due to the fact that the three asymptotes of the spectrum are parallel to the imaginary axis.

  • The expansion of a semigroup and a Riesz basis criterion
    Journal of Differential Equations, 2005
    Co-Authors: Genqi Xu, Siu Pang Yung
    Abstract:

    Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper. Suppose that A is the generator of a C0 semigroup on a Hilbert Space and (A) = 1(A) ∪ 2(A) with 2(A) is consisted of isolated eigenvalues distributed in a vertical strip. It is proved that if 2(A) is separated and for each ∈ 2(A), the dimension of its root subSpace is uniformly bounded, then the generalized eigenvectors associated with 2(A) form an L-basis. Under different conditions on the Riesz projection, the expansion of a semigroup is studied. In particular, a simple criterion for the generalized eigenvectors forming a Riesz basis is given. As an application, a heat exchanger problem with boundary feedback is investigated. It is proved that the heat exchanger system is a Riesz system in a suitable State Hilbert Space.

Genqi Xu - One of the best experts on this subject based on the ideXlab platform.

  • RIESZ BASIS PROPERTY OF TIMOSHENKO BEAMS WITH BOUNDARY FEEDBACK CONTROL
    International Journal of Mathematics and Mathematical Sciences, 2020
    Co-Authors: De-xing Feng, Genqi Xu, Siu Pang Yung
    Abstract:

    A Timoshenko beam equation with boundary feedback control is considered. By an abstract result on the Riesz basis generation for the discrete operators in the Hilbert Spaces, we show that the closed-loop system is a Riesz system, that is, the sequence of generalized eigenvectors of the closed-loop system forms a Riesz basis in the State Hilbert Space.

  • Exponential stability of variable coefficients Rayleigh beams under boundary feedback controls: A Riesz basis approach
    Systems & Control Letters, 2020
    Co-Authors: Jun-min Wang, Genqi Xu, Siu Pang Yung
    Abstract:

    In this paper, we study the boundary stabilizing feedback control problem of Rayleigh beams that have non-homogeneous spatial parameters. We show that no matter how non-homogeneous the Rayleigh beam is, as long as it has positive mass density, stiffness and mass moment of inertia, it can always be exponentially stabilized when the control parameters are properly chosen. The main steps are a detail asymptotic analysis of the spectrum of the system and the proving of that the generalized eigenfunctions of the feedback control system form a Riesz basis in the State Hilbert Space. As a by-product, a conjecture in Guo (J. Optim. Theory Appl. 112(3) (2002) 529) is answered.

  • EXPONENTIAL STABILITY OF TIMOSHENKO BEAM SYSTEM WITH DELAY TERMS IN BOUNDARY FEEDBACKS
    ESAIM: Control Optimisation and Calculus of Variations, 2010
    Co-Authors: Genqi Xu
    Abstract:

    In this paper, the stability of a Timoshenko beam with time delays in the boundary input is studied. The system is fixed at the left end, and at the other end there are feedback controllers, in which time delays exist. We prove that this closed loop system is well-posed. By the complete spectral analysis, we show that there is a sequence of eigenvectors and generalized eigenvectors of the system operator that forms a Riesz basis for the State Hilbert Space. Hence the system satisfies the spectrum determined growth condition. Then we conclude the exponential stability of the system under certain conditions. Finally, we give some simulations to support our results.

  • Stabilization of wave systems with input delay in the boundary control
    ESAIM: Control Optimisation and Calculus of Variations, 2006
    Co-Authors: Genqi Xu, Siu Pang Yung, Leong Kwan Li
    Abstract:

    In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight (1 � µ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the State Hilbert Space. Furthermore, we show that when the weight µ> 1 , for any time delay, we can choose a suitable feedback gain so that the closed loop system is exponentially stable. When µ = 1 ,w e show that the system is at most asymptotically stable. When µ< 1 , the system is always unstable.

  • Exponential Stabilization of Laminated Beams with Structural Damping and Boundary Feedback Controls
    Siam Journal on Control and Optimization, 2005
    Co-Authors: Jun-min Wang, Genqi Xu, Siu Pang Yung
    Abstract:

    We study the boundary stabilization of laminated beams with structural damping which describes the slip occurring at the interface of two-layered objects. By using an invertible matrix function with an eigenvalue parameter and an asymptotic technique for the first order matrix differential equation, we find out an explicit asymptotic formula for the matrix fundamental solutions and then carry out the asymptotic analyses for the eigenpairs. Furthermore, we prove that there is a sequence of generalized eigenfunctions that forms a Riesz basis in the State Hilbert Space, and hence the spectrum determined growth condition holds. Furthermore, exponential stability of the closed-loop system can be deduced from the eigenvalue expressions. In particular, the semigroup generated by the system operator is a $C_0$-group due to the fact that the three asymptotes of the spectrum are parallel to the imaginary axis.

Zouhaïr Mouayn - One of the best experts on this subject based on the ideXlab platform.

  • Phase coherent States with circular Jacobi polynomials for the pseudoharmonic oscillator
    Journal of Mathematical Physics, 2012
    Co-Authors: Zouhaïr Mouayn
    Abstract:

    We construct a class of generalized phase coherent States ∣eiθ; γ, α, ɛ >, indexed by points eiθ of the unit circle and depending on three positive parameters γ, α, and ɛ, by replacing the labeling coefficient zn/n! of the canonical coherent States by circular Jacobi polynomials gnγeiθ with parameter γ ⩾ 0. The special case of γ = 0 corresponds to the well-known phase coherent States. The constructed States are superposition of eigenStates of a one-parameter pseudoharmonic oscillator depending on α and constitute a resolution of the identity of the State Hilbert Space at the limit ɛ → 0+. Closed form for their wavefunctions are obtained in the case α = γ + 1 and their associated coherent States transforms are defined.

  • A new class of coherent States with Meixner?Pollaczek polynomials for the Gol'dman?Krivchenkov Hamiltonian
    Journal of Physics A, 2010
    Co-Authors: Zouhaïr Mouayn
    Abstract:

    A class of generalized coherent States with a new type of the identity resolution is constructed by replacing the labeling parameter of the canonical coherent States by Meixner?Pollaczek polynomials with specific parameters. The constructed coherent States belong to the State Hilbert Space of the Gol'dman?Krivchenkov Hamiltonian.

Naji Yebari - One of the best experts on this subject based on the ideXlab platform.

  • Riesz basis approach and exponential stabilization of a nonhomogeneous flexible beam with a tip mass
    International Journal of Mathematics and Statistics, 2010
    Co-Authors: My Driss Aouragh, Naji Yebari
    Abstract:

    In this paper, we show that there is a sequence of generalized eigenfunctions of an Euler-Bernoulli beam equation with a tip mass which forms a Riesz basis for the State Hilbert Space. Then the exponential stability of the system based on an asymptotic expression of eigenvalues is obtained. A numerical simulation of the spectrum is also presented.

  • Riesz basis approach to the stabilization of a nonuniform Scole model
    International Journal of Mathematics and Statistics, 2010
    Co-Authors: My Driss Aouragh, Naji Yebari
    Abstract:

    In this paper, we consider the uniform stabilization of the well known Scole model with variable coefficients in the case of a clamped beam. We prove that the closed loop system is dissipative. By asymptotic analysis of frequencies of the closed loop system, we give asymptotic expressions of the higher frequencies and we show that a sequence of generalized eigenfunctions of the nonuniform Scole model under boundary feedbacks control forms a Riesz basis for the State Hilbert Space. Numerical results are also presented. This paper is a non uniform version of the results 3 in the case of a clamped beam.

  • Uniform Stabilization of a Hybrid System of Elasticity with Variable Coefficients
    International Journal of Tomography and Simulation, 2008
    Co-Authors: Naji Yebari, Driss Aouragh
    Abstract:

    In the case of a hinged beam we study the boundary feedback stabilization of the well known Scole model with variable coefficients. We show that there is a sequence of generalized eigenfunctions which forms a Riesz basis for the State Hilbert Space. The spectrum determined growth condition, the exponential stability and an asymptotic expression of the spectrum are established. We use a finite difference method to study numerically the spectrum of these boundary operators. Numerical results are also illustrated. This paper generalize the results in [7].

My Driss Aouragh - One of the best experts on this subject based on the ideXlab platform.

  • Uniform Stabilization of a Hybrid System of Elasticity: Riesz Basis Approach
    Differential and Difference Equations with Applications, 2016
    Co-Authors: My Driss Aouragh
    Abstract:

    A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation and a linked rigid body governed by an ordinary differential equation, is considered. This paper studies the basis property and the stability of a hybrid system when the usual linear boundary feedback is applied to the end without mass. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the State Hilbert Space. As consequence expressions of eigenvalues, the spectrum-determined growth condition and the exponential stability are readily presented. To confirm numerically the asymptotic estimate of eigenvalues, we shall use the spectral method to calculate the eigenvalues.

  • Riesz basis approach and exponential stabilization of a nonhomogeneous flexible beam with a tip mass
    International Journal of Mathematics and Statistics, 2010
    Co-Authors: My Driss Aouragh, Naji Yebari
    Abstract:

    In this paper, we show that there is a sequence of generalized eigenfunctions of an Euler-Bernoulli beam equation with a tip mass which forms a Riesz basis for the State Hilbert Space. Then the exponential stability of the system based on an asymptotic expression of eigenvalues is obtained. A numerical simulation of the spectrum is also presented.

  • Riesz basis approach to the stabilization of a nonuniform Scole model
    International Journal of Mathematics and Statistics, 2010
    Co-Authors: My Driss Aouragh, Naji Yebari
    Abstract:

    In this paper, we consider the uniform stabilization of the well known Scole model with variable coefficients in the case of a clamped beam. We prove that the closed loop system is dissipative. By asymptotic analysis of frequencies of the closed loop system, we give asymptotic expressions of the higher frequencies and we show that a sequence of generalized eigenfunctions of the nonuniform Scole model under boundary feedbacks control forms a Riesz basis for the State Hilbert Space. Numerical results are also presented. This paper is a non uniform version of the results 3 in the case of a clamped beam.