Geometric control of patterned linear systems

We introduce and study a new class of linear control systems called patterned systems. Mathematically, this class has the property that the state, input and output transformations of the linear state space model are all functions of a common base transformation. The motivation for studying such systems arises from their interpretation as a collection of identical subsystems with a pattern of interaction between subsystems that is imprinted by the base transformation. The significance of patterned systems as a distinct class is that they may provide a template for the development of a more unified framework for dealing with systems, typically distributed, which consist of subsystems interacting via a fixed pattern.