  This paper presents an overview and comparative study of the state of the art
in State-Order Reduction (SOR) and Scheduling Dimension Reduction (SDR) for
Linear Parameter-Varying (LPV) State-Space (SS) models, comparing and
benchmarking their capabilities, limitations and performance. The use case
chosen for these studies is an interconnected network of nonlinear coupled mass
spring damper systems with three different configurations, where some spring
coefficients are described by arbitrary user-defined static nonlinear
functions. For SOR, the following methods are compared: Linear Time-Invariant
(LTI), LPV and LFR-based balanced reductions, moment matching and
parameter-varying oblique projection. For SDR, the following methods are
compared: Principal Component Analysis (PCA), trajectory PCA, Kernel PCA and
LTI balanced truncation, autoencoders and deep neural network. The comparison
reveals the most suitable reduction methods for the different benchmark
configurations, from which we provide use case SOR and SDR guidelines that can
be used to choose the best reduction method for a given LPV-SS model.
