The algebraic structure of DD systems: a behavioral perspective

This paper presents a survey on the recent contributions to linear time-invariant delaydifferential systems in the behavioral approach. In this survey both systems with commensurate and with incommensurate delays will be considered. The emphasis lies on the investigation of the relationship between various systems descriptions. While this can be understood in a completely algebraic setting for systems with commensurate delays, this is not the case for systems with incommensurate delays. In the study of this class of systems functional analitic methods need to be introduced and general convolutional equations have to be incorporated. Whenever it is possible, the results will be linked to the relevant control theoretic notions.