Global Regulation of Time-Delay Cascade Systems via Partial State Feedback*

The problem of global stabilization is studied by partial state feedback for a class of cascade systems with time-delay. Under suitable ISS conditions on inverse dynamics, a delay-free, dynamic partial state feedback compensator is designed to achieve global state regulation. This is made possible by developing a dynamic gain based design method, together with the ideas of changing supply rates and backstepping. By constructing appropriate Lyapunov-Krasovskii functionals, we prove that all the states of the time-delay cascade system can be regulated to the origin while maintaining boundedness of the closed-loop system.