Predictor feedback and integrator backstepping of linear systems with distributed unbounded delays

This article considers the control problem of linear strict-feedback systems with an infinite-delayed integrator. The integrator backstepping design approach is used to construct a predictor feedback controller. By applying the stability theorem developed in our previous work for systems with unbounded delays, exponential stability of the resulting closed loop system is proved. This article shows that the predictor feedback together with the backstepping design is effective on solving some control problems of systems with unbounded delays. Simulation examples are provided to illustrate the effectiveness of our controller.