Delay effects on stability of interconnected systems. A control perspective

It is well-known that the interconnection of two or more dynamical systems leads to an increasing complexity of the overall system\´s behavior due to the effects induced by the emerging dynamics (in the presence or not of feedback loops) in strong interactions (sensing, communication) with the environment changes. One of the major problems appearing in such interconnection schemes is related to the propagation, transport, and communication delays acting "through" and/or "inside" the interconnections. Without any loss of generality, the origin of such delays can be: the physical separation between the systems defining the interconnections, the presence of the human factor in the decision process, or finally the existence of some hierarchy, and/or synchronization at the lowest levels in the decision process in real-time. The aim of this paper is to present briefly some "user-friendly" methods and techniques (only frequency-domain approaches) for the analysis and control of the dynamical systems in presence of time- delays. The presentation focuses more on the main intuitive (algebraic, geometric) ideas to develop theoretical results, and their potential use in applications.