Structural properties of affine LPV to LFR transformation: Minimality, input-output behavior and identifiability

In this paper, we introduce and study important properties of the transformation of Affine Linear Parameter-Varying (ALPV) state-space representations into Linear Fractional Representations (LFR). More precisely, we show that (i) state minimal ALPV representations yield minimal LFRs, and vice versa, (ii) the input-output behavior of the ALPV representation determines uniquely the input-output behavior of the resulting LFR, (iii) structurally identifiable ALPV models yield structurally identifiable LFRs, and vice versa. We then characterize LFRs which correspond to equivalent ALPV models based on their input-output maps. As illustrated all along the paper, these results have important consequences for identification and control of systems described by LFRs.