Symmetries of Autonomous Linear Control Systems

Abstract

This paper is concerned with symmetry and identification problems for time-optimal linear autonomous control systems in Euclidean space. A symmetry is a nonsingular linear transformation which reproduces each of the reachable sets. Under rather general conditions all the symmetries of a control system are described constructively (Theorem 4). In an analogous situation, it is determined when two control systems have the same reachable sets; the identification problem (Theorem 6). Both of these are special cases of a wider result (Theorem 3) which may well be amenable to further generalization.