Benefits of the Input Minimum Phase Property for Linearization of Nonlinear Systems, Report no. LiTH-ISY-R-2720

Linear approximations of nonlinear systems can be obtained by fitting a linear model to data from a nonlinear system, for example, using the prediction-error method. In many situations, the type of linear model and the model orders are selected after estimating several models and evaluating them using various validation techniques. Two commonly used validation methods for linear models are spectral and residual analysis. Unfortunately, these methods will not always work if the true system is nonlinear. However, if the input can be viewed as if it has been generated by filtering white noise through a minimum phase filter, spectral and residual analysis can be used for validation of linear models of nonlinear systems. Furthermore, it can be shown that the input minimum phase property guarantees that a certain optimality result will hold. Here, the benefits of using minimum phase instead of non-minimum phase filters for input design will be shown both theoretically and in numerical experiments.