Stability and stabilization of systems with time delay

Control systems often operate in the presence of delays, primarily due to the time it takes to acquire the information needed for decision-making, to create control decisions, and to execute these decisions, as shown in Figure 1. Systems with delays arise in engineering, biology, physics, operations research, and economics. In traffic-flow models, the drivers ’ delayed reactions, which combine sens-ing, perception, response, selection, and programming delays, must be con-sidered [1–3]. These delays are critical in accounting for human behavior, analyzing traffic-flow stability, and designing collision-free traffic flow using adaptive cruise controllers [4]. Material distribution and supply-chain systems are composed of inter-connected supply-demand points that share products and information in order to regulate inventories and respond to customer demands [5]. Sources of delay in supply chains include decision-making, transportation-line deliv-ery, and manufacturing facilities that work with lead times [6]. These delays