Identification of the symmetries of linear systems with polytopic constraints

In this paper we consider the problem of finding all the state-space and input-space transformations that preserve the parameters of a constrained linear system. Such transformations are called symmetries. For systems constrained by bounded polytopes the set of all symmetries is a finite group and requires techniques from discrete mathematics to find. We transform the problem of finding the symmetries of a constrained linear system into the problem of finding the symmetries of a vertex colored graph. The symmetries of a vertex colored graph can be found efficiently using graph automorphism software. We demonstrate our symmetry identification procedure on a quadcopter example.