On Local LTI Model Coherence for LPV Interpolation

In the local approach to linear parameter varying (LPV) system identification, it is widely acknowledged that locally estimated linear state-space models should be made coherent before being interpolated, but the accurate meaning of the term "coherent" or "coherence" is rarely defined. The purpose of this article is to analyze the relevance of two existing definitions and to point out the consequence of this analysis on the practice of LPV system identification.