Abstract
This paper considers stabilization of linear systems cascaded with a chain of infinite-delayed integrators. Distributed infinite input delay is also taken into consideration. The systems under consideration can be seen as a special class of linear strict-feedback systems with infinite delays. A novel predictor feedback controller is proposed via an n-step backstepping procedure. The Lyapunov theorem developed for infinite-delayed systems in our previous work is applied. It is shown that the proposed controller can globally stabilize the concerned systems. To our best knowledge, it is a first work on control of systems with simultaneous distributed infinite state and input delays. A simulation example is provided to illustrate the effectiveness of our controller.
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