Comparing global input-output behavior of frozen-equivalent LPV state-space models
This addresses a theoretical gap for control engineers using LPV models, but the result is incremental as it formalizes known intuition.
The paper provides an analytic error bound on the difference between input-output behaviors of two frozen-equivalent LPV models, showing the difference can be made arbitrarily small by choosing a slowly varying scheduling signal.
It is known that in general, \emph{frozen equivalent} (Linear Parameter-Varying) LPV models, \emph{i.e.}, LPV models which have the same input-output behavior for each constant scheduling signal, might exhibit different input-output behavior for non-constant scheduling signals. In this paper, we provide an analytic error bound on the difference between the input-output behaviors of two LPV models which are frozen equivalent. This error bound turns out to be a function of both the speed of the change of the scheduling signal and the discrepancy between the coherent bases of the two LPV models. In particular, the difference between the outputs of the two models can be made arbitrarily small by choosing a scheduling signal which changes slowly enough. An illustrative example is presented to show that the choice of the scheduling signal can reduce the difference between the input-output behaviors of frozen-equivalent LPV models.