Performance output tracking for a 1-D unstable Schrödinger equation with input delay

In this paper, we investigate the performance output tracking for a one-dimensional unstable Schrödinger equation with input delay and disturbance, in which the control input is subject to a time delay. Both the performance output and the disturbance are non-collocated to the controller. By writing the time delay as a first-order hyperbolic equation, the control system can be modeled as a cascade construction in which the transport equation can be regarded as the actuator dynamics of the unstable wave equation. With the help of the actuator dynamics compensation, the difficulties caused by input delay are addressed. The full state feedback law is constructed to achieve the performance output tracking and an error based observer is designed successfully. The exponential stability of the closed-loop system is obtained.