Controllers in the linear parameter-varying (LPV) framework are commonly designed in continuous time (CT) requiring accurate and low-order CT models of the system. However, identification of CT-LPV models is largely unsolved, representing a gap between the available LPV identification methods and the needs of control synthesis. In order to bridge this gap, direct identification of CT-LPV systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive discrete-time (DT) coloured noise process. To provide consistent model parameter estimates in this setting, a refined instrumental variable (IV) approach is proposed and its properties are analysed based on the prediction-error framework. The benefits of the introduced direct CT-IV approach over identification in the DT case are demonstrated through a representative simulation example inspired by the Rao-Garnier benchmark.
Laurain, V., Toth, R., Gilson, M., & Garnier, H. (2011). Direct identification of continuous-time linear parameter-varying input/output models. IET Control Theory & Applications, 5(7), 878-888. https://doi.org/10.1049/iet-cta.2010.0218