Realisation and estimation of piecewise-linear output-error models

Piecewise-linear systems in input/output form can have different switching schedules. In this article, two categories, instant and delayed switching, are analysed. Even though a general piecewise-linear state-space model cannot be converted into input/output form, it is shown that it is possible to find state-space models representing instant and delayed switching. In addition, a prediction-error minimisation (PEM) method for piecewise-linear output-error predictors is derived and it is concluded that the instant-switching model candidate is not necessarily the most suitable for the parameter estimation procedure.