### 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.

Original language | English |
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Title of host publication | Proceedings of the the 2011 American Control Conference (ACC 2011), June 29 - July 1, 2011, San Francisco, California |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Publication status | Published - 2011 |

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## Cite this

Lombardi, W., Olaru, S., Lazar, M., & Niculescu, S-I. (2011). On positive invariance for delay difference equations. In

*Proceedings of the the 2011 American Control Conference (ACC 2011), June 29 - July 1, 2011, San Francisco, California*Institute of Electrical and Electronics Engineers.