Linear parameter-varying subspace identification: A unified framework

In this paper, we establish a unified framework for subspace identification (SID) of linear parameter-varying (LPV) systems to estimate LPV state–space (SS) models in innovation form. This enables us derive novel SID schemes that are extensions existing time-invariant (LTI) methods. More specifically, the open-loop, closed-loop, and predictor-based data-equations (input–output surrogate forms SS representation) by systematically establishing an theory. We also show additional challenges setting compared LTI case. Based on data-equations, several methods proposed LPV-SS based maximum-likelihood or realization argument. Furthermore, established theoretical problem allows lower number to-be-estimated parameters overcome dimensionality problems involved matrices, leading decrease computational complexity SIDs general. To authors’ knowledge, paper is first in-depth examination problem. The effectiveness demonstrated with Monte Carlo study identifying benchmark MIMO system.