Output feedback stabilization of an unstable wave equation with observations subject to time delay
This paper focuses on boundary stabilization of a one dimensional wave equation with an unstable boundary condition, in which observations are subject to arbitrary fixed time delay. The observability inequality indicates that the open loop system is observable, based on which the observer and predictor are designed: The state of system is estimated with available observation and then predicted without observation. After that equivalently the authors transform the original system to the well posed and exponentially stable system by backstepping method. The equivalent system together with the design of observer and predictor give the estimated output feedback. It is shown that the closed loop system is exponentially stable. Numerical simulations are presented to illustrate the effect of the stabilizing controller.
J. Syst. Sci. Complex.