A branch of control theory concerned with large-scale systems. The three commonly accepted definitions of a large-scale system are based on notions of decomposition, complexity, and centrality. A system is sometimes considered to be large-scale if it can be partitioned or decomposed into small-scale subsystems. Another definition is that a system is large-scale if it is complex; that is, conventional techniques of modeling, analysis, control, design, and computation do not give reasonable solutions with reasonable effort. A third definition is based on the notion of centrality. Until the advent of large-scale systems, almost all control systems analysis and design procedures were limited to components and information grouped in one geographical location or center. Thus, by another definition, a system in which the concept of centrality fails is large-scale. This can be due to a lack of either centralized computing capability or a centralized information structure. Large-scale systems appear in such diversified fields as sociology, management, the economy, the environment, computer networks, power systems, transportation, aerospace, robotics, manufacturing, and navigation. Some examples of large-scale systems are the United States economy, the global telephone communication network, and the electric power generation system for the western United States. See Control systems, Systems engineering