Loop transfer recovery for systems under sampled measurements

The paper addresses the problem of loop transfer recovery (LTR) of continuous-time systems with sampled output measurements, that is, given an ideal (desired) continuous-time linear state feedback controller, the authors seek for a dynamic output feedback controller based on sampled measurements, such that the state feedback control is best approximated in a certain sense for robustness reasons. They first point out a simple fact that the so-called exact or asymptotic LTR is not possible for such sampled-data systems when the intersampling response is taken into account, regardless of the relative degree and mininium-phase properties and the sampling rate of the system. Based on this observation, the authors proceed to formulate a generalised loop transfer recovery problem which searches for an optimal dynamic output feedback controller which minimises the difference between the target loop transfer function and the output feedback based one in some H-infinity sense. The main result then is to show that this generalised LTR problem is equivalent to a known filtering problem for sampled-data systems, which is solved in terms of a pair of differential and difference Riccati equations.