On hyper-exponential output-feedback stabilization of a double integrator by using artificial delay

The problem of output-feedback stabilization of a double integrator is revisited with the objective of achieving the rates of convergence faster than exponential. It is assumed that only position is available for measurements, and the designed feedback is based on the output and its delayed values without anestimationofvelocity. It is shown that by selecting the closed loop system to be homogeneous with negative or positive degree it is possible to accelerate the rate of convergence in the system at the price of a small steady-state error. Efficiency of the proposed control is demonstrated in simulations.