Output feedback stabilization of an unstable wave equation with observations subject to time delay

Output Feedback Stabilization of Unstable Heat Equations with Time Delay in Boundary Observation

“…where 􏽢 w 0 is the initial value of the observer (8), w 0 is the initial value of the original system (1), and M, ω and M 1 , ω 1 are constants in (13) and (23), respectively.…”

“…In the past decades, much effort has been made for the problems of unstable or antistable infinite-dimensional systems which can be applied to practical engineering (see [1][2][3][4][5][6][7][8][9][10][11][12][13]). For example, reference [14] relates the loss of the heat to the surrounding medium and the destabilizing heat generation inside the rod.…”

“…For example, Kang and Guo [6] consider boundary stabilization for a cascade of unstable heat PDE systems where an output feedback is designed by the backstepping transformation. Moreover, reference [13] has applied the backstepping transformation to overcome the destabilizing boundary condition for a wave equation. e predictor-based feedback control may be an effective method to make the unstable reaction-diffusion equation compensate the delay (see [7,11]).…”