On positive invariance for delay difference equations

Abstract

In this paper a new concept of set invariance, called D-invariance, is introduced for dynamical systems described by delay difference equations. We will be interested in the definition and computation of such invariant sets in a specified bounded region of the state-space. The Minkowski algebra will be used to define mappings over the set of compact sets in direct relationship with the invariance of time-delay systems. Set-iterates based on these mappings can be used for the construction of a non-decreasing sequence of D-invariant sets.