Spatio-temporal symmetries in linear control systems with an application to formation control

We study a class of controlled linear systems characterized by a property of spatio-temporal symmetry. We study its stabilizability and detectability properties. We present a design technique to locally stabilize spatio-temporally symmetric orbits of equivariant systems, that has applications in the control of identical interconnected systems. As an example, we present the stabilization of a formation of unicycle robots in cyclic pursuit.