Stabilization of one-dimensional wave equation by non-collocated boundary feedback

In this paper, we are concerned with the stabilization of a one-dimensional wave equation with non-collocated actuator/sensor configuration. A brand-new output feedback law is proposed by a completely new transformation. Different from the previous research, the proposed controller is not observer-based and the output measurement suffers from a constant time delay. It is proved that the resulting closed-loop system is exponentially stable. Some numerical simulations are presented to validate this theoretical result.