Prescribed-Time Output-Feedback Stabilization of Uncertain Nonlinear Systems with Unknown Time Delays

A prescribed-time output-feedback stabilizing controller is designed for a class of uncertain nonlinear strict-feedback-like systems with unknown time delays. The control design is based on a novel adaptation of the dual dynamic high-gain scaling based observer and controller design methodology wherein a Lyapunov-Krasovskii functional is first used to show existence of closed-loop solutions over the prescribed time interval. Thereafter, dynamics of an adaptation state variable and high-gain scaling parameter are used to show that unknown parameters are dominated within a sub-interval of the prescribed time after which a formulation of a Lyapunov function dynamics as a scalar delay differential equation is introduced to establish exponential convergence within the remaining sub-interval of the prescribed time.