Robust Minimum-time Constrained Control of Nonlinear Discrete-Time Systems: New Results

This work deals with the analysis and the design of robust minimum-time control laws for nonlinear discrete-time systems with possibly non robustly controllable target sets. Given a Lipschitz nonlinear transition map with bounded control inputs, in the paper we show that the reachability properties of the target set can be used to assess the existence of a robust positively controllable set which includes the target in its interior. This result is exploited to formulate a minimum-time control scheme with enhanced robustness properties able to ensure the ultimate boundedness of the state-trajectories in presence of bounded uncertainties even in the case in which the target set is not robustly positively controllable.