Design of observer-based controllers for LPV systems with unknown parameters

Output-based feedback control of LPV systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. In this paper we consider this problem in the case of discrete-time LPV systems for which the parameters are not exactly known, but only available with a finite accuracy or affected by noise during their measurement. The controllers are obtained using a separate design of an observer and a state feedback and the interconnection is proven to stabilize the LPV system despite the mismatch between the true and available parameters. The approach allows to maximize the parameter uncertainty while still guaranteeing closed-loop stability. In addition, it is possible to make tradeoffs between the admissible level of mismatch on the one hand and the performance in terms of decay factors on the other. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustrated by a numerical example.