Prescribed-Time Stabilization of Controllable Arbitrary Order Systems Using Switched State Feedback

A novel switched state feedback is proposed to stabilize an arbitrary order chain of integrators in prescribed time regardless of matched external disturbances with an a priori known magnitude bound. The design recast a HOSM (high order sliding mode) controller with finite-time convergence to the origin, especially developed for a system composed of diagonal and over-diagonal forms, and it is based on the scaling technique. The proposed hybrid control algorithm operates with time-varying gains, uniformly bounded on an infinite horizon, thereby yielding an attractive implementation opportunity compared to the original design [1] with time-varying gains, which escape to infinity as time goes to the prescribed time instant. Capabilities of the present hybrid control algorithm are supported in a numerical study, performed for a perturbed triple integrator, and are compared with existing prescribed-time and fixed-time controllers.