Detection and quantification of dynamic dependence in linear parameter-varying differential equations

In the identification of linear parameter-varying models, it is usually assumed that the model coefficients vary instantaneously with the external scheduling parameter. Any dynamics in the model coefficients with respect to the scheduling are therefore neglected. In this paper, we propose a method to detect and quantify the dynamic dependence of the coefficient functions. Proceeding in this way, it can be verified whether the scheduling dynamics are indeed negligible. First, a general linear time-varying model is identified. Subsequently, the covariance of the estimated model parameters is calculated, which allows the computation of a confidence bound for the coefficient functions. Eventually, it is determined whether the dynamic dependence on the scheduling parameter falls in this confidence bound and, thus, whether it is justifiable to use a model with a static dependence on the scheduling parameter.