Time-delay systems: an overview of some recent advances and open problems

After presenting some motivations for the study of time-delay system, this paper recalls modifications (models, stability, structure) arising from the presence of the delay phenomenon. A brief overview of some control approaches is then provided, the sliding mode and time-delay controls in particular. Lastly, some open problems are discussed: the constructive use of the delayed inputs, the digital implementation of distributed delays, the control via the delay, and the handling of information related to the delay value.