Adaptive stabilization of LTI systems with distributed input delay

SUMMARY We solve stabilization problems of LTI systems with unknown parameters and distributed input delay. The key challenge is that the infinite‐dimensional input dynamics are distributed, which makes traditional infinite‐dimensional backstepping inapplicable. We resolve this challenge by employing backstepping–forwarding transformations of the finite‐dimensional state of the plant and of the infinite‐dimensional actuator state. These transformations enable us to design Lyapunov‐based update laws. We also design an adaptive controller for rejecting a constant disturbance in the input of the LTI plant, in the case where the parameters of the plant are known.