Prescribed-time stabilization of nonlinear systems with uncertainties/disturbances by improved time-varying feedback control

We address the prescribed-time stability of a class of nonlinear system with uncertainty/disturbance. With the help of the parametric Lyapunov equation (PLE), we designed a state feedback control to regulate the full-state of a controlled system within prescribed time, independent of initial conditions. The result illustrated that the controlled state converges to zero as $t$ approaches the settling time and remains zero thereafter. It was further proved that the controller is bounded by a constant that depends on the system state. A numerical example is presented to verify the validity of the theoretical results.