Adaptive stabilization of delay differential systems with unknown uncertainty bounds

Based on output measurements, two feedback control schemes are developed for robust stabilization of a wide class of non-linear uncertain delay differential systems with time-varying state delay. The parameters of the adaptive controller are updated robustly when the bounds of the uncertainties are unknown. Both schemes are proved to render the controlled system globally practically stable. The developed controller is demonstrated in a water-quality model for the purpose of preserving standards of water constituents in streams.