Forwarding, backstepping, and finite spectrum assignment for time delay systems

The nonlinear control ideas and results of forwarding and backstepping have been recently extended to systems with time delay. In this paper we discuss how to apply these tools to design robust controls for linear delay systems. We first show that the integral cross-term forwarding produces a feedback law that achieves finite spectrum of the closed loop system. Combining it with backstepping provides a structured design method for a large class of systems with time delay. Robustness of the controller to uncertainties, including uncertain time delay, is illustrated by an example.