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.