Time-varying feedback for stabilization in prescribed finite time

This paper provides a time-varying feedback alternative to control of finite-time systems, which is referred to as “prescribed-time control,” exhibiting several superior features: (i) such time-varying gain–based prescribed-time control is built upon regular state feedback rather than fractional-power state feedback, thus resulting in smooth (Cm) control action everywhere during the entire operation of the system; (ii) the prescribed-time control is characterized with uniformly prespecifiable convergence time that can be preassigned as needed within the physically allowable range, making it literally different from not only the traditional finite-time control (where the finite settling time is determined by a system initial condition and a number of design parameters) but also the fixed-time control (where the settling time is subject to certain constraints and thus can only be specified within the corresponding range); and (iii) the prescribed-time control relies only on regular Lyapunov differential inequality instead of fractional Lyapunov differential inequality for stability analysis and thus avoids the difficulty in controller design and stability analysis encountered in the traditional finite-time control for high-order systems.