Discretization of Linear Fractional Representations of LPV systems

TLDR: The proposed and existing methods are compared and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling, and criteria to choose appropriate sampling times with respect to the investigated methods are presented.

Abstract: Commonly, controllers for Linear Parameter- Varying (LPV) systems are designed in continuous-time using a Linear Fractional Representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from continuous-time first-principle models. Existing discretization approaches for LFRs suffer from disadvantages like alternation of dynamics, complexity, etc. To overcome the disadvantages, novel discretization methods are derived. These approaches are compared to existing techniques and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling.