Nonsmooth control of time-delay nonlinear systems by dynamic state feedback

We study the problem of global state feedback control for a class of time-delay uncertain systems. Under mild regularity conditions on the system nonlinearities involving time delay, a delay-independent, non-smooth dynamic state compensator is constructed by developing a dynamic gain based design method. Using appropriate Lyapunov-Krasovskii functionals, we prove that all the states of the time-delay nonlinear system can be regulated to the origin while maintaining boundedness of the closed-loop system. As a byproduct of this development, adaptive regulation of the same class of nonlinearly parameterized systems with time-delay is also shown to be possible, via a similar Lyapunov-Krasovskii design method. Two examples are presented to validate the effectiveness of the proposed non-smooth feedback controllers.