LPV-ARX representations of LPV state-space models with affine dependence

In this paper, we show that an input–output map can be realized by a linear parameter-varying (LPV) state-space representation with affine and static dependence on the scheduling variables, if only satisfies certain LPV autoregressive equations. The latter class of equations is in derivatives (for continuous-time) or time-shifts discrete-time) outputs control inputs, while coefficients equation are polynomials shifts variable discrete-time, high-order continuous-time. This result generalization well-known equivalence between representations models. Moreover, extends results Tóth (2010) dynamic meromorphic variables to variables.