Stabilization via Iterative State Steering with Application to Chained-Form Systems

A general approach is presented for the robust stabilization of controllable systems. The proposed strategy is viable whenever one can compute a finite-time control law that steers the state from any initial condition to a point closer to the desired equilibrium. Under suitable hypotheses, such control law can be applied in an iterative fashion, obtaining exponential convergence of the state to the equilibrium point. Moreover, small nonpersistent perturbations are rejected, while small persistent perturbations induce limited errors. The proposed approach is applied to chained-form systems and simulations are presented for a unicycle.