State-Space realization of LPV Input-Output models: practical methods for the user

Identification of Linear Parameter-Varying (LPV) systems is often accomplished via Input-Output (IO) model structures in discrete-time. This approach is common because of its simplicity and the possibility to extend identification methods for Linear Time-Invariant (LTI) systems. However, a realization of LPV-IO models as State-Space (SS) representations, often required for control synthesis, is complicated due to the phenomenon of dynamic dependence (dependence of the resulting representation on time-shifted versions of the scheduling signal). This conversion problem is revisited and practically applicable approaches are suggested which result in SS representations that have only static dependence (dependence on the instantaneous value of the scheduling signal). To reduce complexity, a criterion is established to decide when an LTI type of realization can be used without introducing significant error. To reduce the order of the resulting SS realization, a LPV Ho-Kalman type of model reduction approach is introduced, which is capable of reducing even unstable models. The proposed methods are illustrated by application oriented examples.