Dynamic stabilization of an Euler–Bernoulli beam equation with time delay in boundary observation

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

“…It is seen that the displacement is not convergent anymore. This phenomena coincides with [13] for beam equation. The big difference with [13] is that we are able to show the convergence for non-smooth initial values.…”

“…This phenomena coincides with [13] for beam equation. The big difference with [13] is that we are able to show the convergence for non-smooth initial values. The scheme is certainly applicable to multi-dimensional PDEs and we believe that the same convergence is also true in that case.…”

“…The idea behind is to use the infinite-dimensional observer to recover the state. In the presence of time delay, we used in [13] the same idea for Euler-Bernoulli beam equation: The state is estimated by the observer in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. Unfortunately, the convergence is only proved for smooth initial values in [13].…”

“…In the presence of time delay, we used in [13] the same idea for Euler-Bernoulli beam equation: The state is estimated by the observer in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. Unfortunately, the convergence is only proved for smooth initial values in [13]. One of main objectives of this paper is to deal with the convergence of the scheme for one-dimensional wave equation when the initial values are not smooth.…”

Exponential Stability of the Monotubular Heat Exchanger Equation with Time Delay in Boundary Observation

“…However, this does not mean that there is no stabilizing controller in the presence of time delay. You can refer to [12][13][14][15][16][17][18] for some successful examples.…”