On decentralisation, symmetry and special structure in linear systems

Many systems in nature and engineering (linear dynamical input/output systems in state space form) have a good deal of special structure. They may consist of a collection of identical units connected together in various ways, or there may be large systems consisting of many submits which fall into a small number of types; for example, think of electrical or neural networks. Another example consists of two helicopters connected with a rigid beam, a system which is of considerable importance for practical applications and, as we shall see, which poses many unsolved problems. Other examples arise from the discretization (in space) of partial differential equations [Brockett-Willems, 1974].