Dynamic partial state feedback control of cascade systems with time-delay

This paper investigates the problem of global stabilization by partial state feedback for a class of cascade nonlinear systems with time-delay. Under suitable ISS conditions imposed on zero-dynamics, a delay-free, dynamic partial state feedback compensator is presented for achieving global state regulation. The controller is constructed by employing a dynamic gain based design method, together with the ideas of changing supply rates and adding an integrator. With appropriate choices of Lyapunov-Krasovskii functionals, it is shown that all the states of the time-delay cascade system can be regulated to the origin while maintaining boundedness of the closed-loop system. Two examples are given to illustrate the effectiveness of the proposed dynamic partial state feedback control scheme.