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...
We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build all the above-mentioned...
We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the...
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...
We intend to conduct a fairly complete study on
Timoshenko beams with pointwise feedback controls and seek to obtain information
about the eigenvalues, eigenfunctions, Riesz-Basis-Property,
spectrum-determined-growth-condition, energy decay rate and various stabilities
for the beams. One major difficulty of the present problem is the non-simplicity
of the eigenvalues.
In fact, we shall indicate in this paper situations where the multiplicity of
the eigenvalues is at least two. We build all the...
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 is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system
generates a
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...
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