Practical Prescribed-Time Stabilization and Tracking for Uncertain Nonlinear Systems with Disturbance Inputs

We develop an output-feedback control design that achieves practical prescribed-time stabilization, i.e., convergence to within a pre-specified neighborhood around the origin within a pre-specified ("prescribed") time interval. The control design is applicable to a class of uncertain nonlinear systems in a strict-feedback-like form with parametric and functional uncertainties throughout the system as well as exogenous disturbance inputs. The designed output-feedback control design achieves prescribed-time convergence of both the observer errors and the system state variables as well as the control input. Additionally, by considering the limiting case as the size of the desired convergence neighborhood around the origin is reduced to zero, it is shown that the prior results on prescribed-time stabilization (to zero in prescribed time) can be obtained without having to explicitly introduce the temporal scale transformation used in the prior works. It is also shown that the control design approach can be applied to tracking problems to achieve practical convergence of tracking errors.