Prescribed-Time Semi-Global Control for a Class of Nonlinear Uncertain Systems by Linear Time-Varying Feedback

The prescribed-time semi-global control for a class of time-varying uncertain systems under a nonlinear growth condition is achieved via linear time-varying feedback. The involved nonlinear uncertainties are categorized as unmatched uncertainties (depending on states and time) and matched uncertainties (depending on time only). Both state feedback and observer-based output feedback are constructed relying on the properties of parametric Lyapunov equations and the time-varying gains acquired by solving scalar differential equations. The proposed output feedback approach features a separation principle, that is, the construction of prescribed-time observer and prescribed-time state feedback is conducted separately. The proposed control scheme is validated by simulations carried out on a standard mechatronics system with complicated loads.