On the construction of D-invariant sets for linear polytopic delay difference inclusions

摘要

The construction of model predictive control schemes for linear polytopic delay difference inclusions (lpDDIs) is a complex task, especially for lpDDIs with large or time-varying delays. The main challenge is to formulate a control scheme that is computationally tractable. A first step towards such a control scheme is the construction of a set with particular invariance properties, called D-invariance, which allows to formulate the controller for a relatively low-dimensional system and guarantees a type of delay-independent invariance. Therefore, necessary and sufficient conditions for the existence of a D-invariant set are presented in this paper. Furthermore, synthesis algorithms for both polyhedral and ellipsoidal D-invariant sets are also derived. The applicability of the proposed results is illustrated via an example.