Prescribed-Time Stabilization of Controllable Planar Systems Using Switched State Feedback

A novel switched state feedback is proposed to stabilize a planar controllable system in prescribed time regardless of whichever uniformly bounded external disturbance affects the system. The approach is based on a successive application of time-varying linear feedback synthesis and twisting controller design. The underlying strategy is to utilize globally stabilizing non-autonomous linear feedback so that the system trajectories enter an arbitrarily small domain of attraction as fast as desired regardless of initial conditions and then switch to the twisting controller that settles the trajectories from the pre-specified attraction domain at the origin in prescribed time. Tuning rules to achieve the desired settling time are explicitly derived and illustrated in an experimental study of a simple pendulum to track a reference trajectory with periodic velocity jumps.