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It is known that in general, \emph{frozen equivalent} (LinearParameter-Varying) LPV models, \emph{i.e.}, LPV models which have the sameinput-output behavior for each constant scheduling signal, might exhibitdifferent input-output behavior for non-constant scheduling signals. In thispaper, we provide an analytic error bound on the difference between theinput-output behaviors of two LPV models which are frozen equivalent. Thiserror bound turns out to be a function of both the speed of the change of thescheduling signal and the discrepancy between the coherent bases of the two LPVmodels. In particular, the difference between the outputs of the two models canbe made arbitrarily small by choosing a scheduling signal which changes slowlyenough. An illustrative example is presented to show that the choice of thescheduling signal can reduce the difference between the input-output behaviorsof frozen-equivalent LPV models.

Comparing global input-output behavior of frozen-equivalent LPV state-space models