Direct Identification of Continuous-Time LPV Input/Output Models

Controllers in the linear parameter-varying (LPV) framework are commonly designed in continuoustime (CT) requiring accurate and low-order CT models of the system. However, identification of continuous-time 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 colored noise process. To provide consistent model parameter estimates in this setting, a refined instrumental variable (IV) approach is proposed and its properties are analyzed based on the prediction-error framework. The benefits of the introduced direct CT-IV approach over identification in the discrete-time case are demonstrated through a representative simulation example inspired by the Rao-Garnier benchmark. Index Terms Continuous-time models, LPV models, system identification, refined instrumental variable, Box– Jenkins models, input/output.