Continuous-time controller redesign for digital implementation: A trajectory based approach

Given a continuous time nonlinear closed loop system, we investigate sampled–data feedback laws for which the trajectories of the sampled–data closed loop system converge to the continuous time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero. We derive necessary and sufficient conditions for the existence of such sampled–data feedback laws and — in case of existence — provide explicit redesign formulas and algorithms for these controllers.