Delays effects in dynamical systems and networks: Analysis and control interpretations

Abstract

Time-delays are important components of many systems from engineering, economics and the life sciences, due to the fact that the transfer of material, energy and information is mostly not instantaneous. They appear for instance as computation and communication lags, they model transport phenomena and hereditary effects and they arise as feedback delays in control loops. The aim of the chapter is to present a guided tour on stand-alone and interconnected systems with delays, thereby explaining some important qualitative properties. The focus rather lies on the main ideas as technical details are avoided. Different mechanisms with which delays can interact with the system are outlined, with the emphasis on the effects of delays on stability. It is clarified how these mechanisms affect control design problems. Not only limitations induced by delays in control loops are discussed, but also opportunities to use delays in the construction of controllers. Finally, extensions of these results toward networks of interconnected dynamical systems are discussed, with the focus on relative stability problems, in particular the synchronization problem.