Time-scale separation redesign for stabilisation and performance recovery of sampled-data non-linear systems

This study addresses semi-global practical asymptotic stabilisation and performance recovery of a class of sampled-data non-linear systems using a time-scale separation redesign. In particular, a high-gain filter is designed to estimate uncertainties in continuous-time and a fast variable coming from the filter is used to cancel the effect of the uncertainty, then the controller including the filter is descritised in Euler method. The authors provide conditions relating the sampling time and the filter gain, with which the results for the sampled-data system are the same as those that have been developed for the continuous-time system. As a verification of results, numerical simulations are given.