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In this paper we study asymptotic behaviour of distributed parameter systems governed
by partial differential equations (abbreviated to PDE). We first review some recently developed results
on the stability analysis of PDE systems by Lyapunov's second method. On constructing Lyapunov functionals
we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE
systems. Then we apply the result to establish exponential stability of various chemical engineering
processes...
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...
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...
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