Frequency response functions of linear parameter-varying systems

Frequency-domain system representations offer important system analysis, control design and simulation tools. While this representation concept is well developed for linear time-invariant systems, there has been no general theory established for the linear parameter-varying (LPV) system class. This paper overviews and compares the existing concepts of frozen and instantaneous frequency-domain LPV representations, pointing out the need for a representation form where the effect of the spectrum of a varying scheduling trajectory can be clearly understood and analyzed on the output spectrum. For this purpose, the harmonic frequency response function (hFRF), known from the linear time-varying literature, in introduced for LPV systems. More specifically the paper demonstrates how the hFRF can be computed directly in the frequency domain for discrete-time affine input-output LPV systems.