Adaptive Regulation of Time-Delay Cascade Systems with Parameter Uncertainty

Under a suitable condition on the zero-dynamics with time-delay, we prove that global state regulation can be achieved by a partial state adaptive controller for certain time-delay cascade systems with unknown parameters. A delay-independent, partial state adaptive control scheme is developed based on a dynamic gain-based design, the idea of changing supply rate and the feedback domination approach. With the help of appropriate Lyapunov-Krasovskii functionals, it is shown that the resulting closed-loop system is globally bounded and all the states of the time-delay cascade system converge to the origin.