Global prescribed-time output feedback regulation of nonlinear systems with unknown and unbounded measurement sensitivity

Prescribed-time control guarantees system convergence within a user-specified finite time, making it particularly suitable for time-critical applications. However, most existing approaches rely on accurate state measurements or bounded uncertainties, thereby limiting their practical applicability. This paper addresses the prescribed-time regulation problem for nonlinear systems with unknown and potentially unbounded measurement sensitivity, as well as an unknown nonlinear growth rate, which has not been investigated in the existing literature. To this end, a novel dynamic-gain prescribed-time output feedback controller is developed by integrating a prescribed-time function into a Lyapunov-based backstepping framework. The proposed controller achieves robust regulation without requiring prior knowledge of either the system nonlinearities or the measurement sensitivity, thereby extending the applicability of prescribed-time control to a broader class of uncertain nonlinear systems.