On discretization of continuous-time LPV control solutions

Abstract

In recent years, the Linear Parameter-Varying (LPV) framework has become increasingly useful for analysis and control of time-varying systems. Generally, LPV control synthesis is performed in the continuous-time (CT) domain due to significantly more intuitive performance shaping methods in CT. However, the main complication of CT synthesis approaches is the successive implementation of the resulting CT control solutions on physical hardware. In the literature, several discretization methods have been developed for LPV systems. However, most of these approaches necessitate heavy nonlinear operations introduced by the discretization of these time-varying matrices or can introduce significant approximation error, thereby severely limiting implementation capabilities of CT LPV control solutions. Alternatively, the $w'$ discretization approach has been introduced in the LTI case to allow for preservation of the CT control. Based on these observations, this paper aims at extending the $w'$ discretization approach to LPV systems, such that implementation of CT LPV control solutions on physical hardware is simplified.