Predictor-feedback for multi-input LTI systems with distinct delays

In this paper, we propose a predictor-based state feedback controller for multi-input linear time-invariant systems with different time delays in each individual input channel. The controller is designed based on the backstepping method. Since the conventional backstepping transformation is not applicable to the systems due to the differences among delays, a modified transformation is introduced. This transformation enables us to design an exponentially stabilizing controller under which the plant behaves as if the delay were absent after a finite time interval. In addition, an explicit Lyapunov functional is constructed. The performance of the controller is demonstrated by a numerical simulation.