On discretization of continuous-time LPV control solutions

TL;DR

This paper extends the $w'$ discretization method to LPV systems, enabling simpler implementation of continuous-time LPV control solutions on hardware by reducing approximation errors and nonlinear operations.

Contribution

It introduces an extension of the $w'$ discretization approach specifically for LPV systems, facilitating more accurate and hardware-friendly implementation of CT control solutions.

Findings

Extended $w'$ discretization preserves CT control in LPV systems.

Reduces approximation errors compared to existing discretization methods.

Simplifies implementation of LPV control solutions on physical hardware.

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.