| Abstract: | Two constant linear systems are said to be feedback equivalent if one can be transformed into the other via an element of the “feedback group”, which acts by state space feedback and by change of basis in the state and input spaces. Let Cn,m be the space of n-dimensional completely reachable systems with m-dimensional input (pairs of matrices, n × n and n × m). The action of the feedback group partitions the space Cn,m into finitely many orbits (equivalence classes), and the closure of each orbit is a union of orbits. If one views orbit closure as ‘deformation’, then orbit closure may be considered in terms of perturbations or system failure. In this paper we determine: (1) a classification of the orbits, and (2) the orbits contained in the closure of a given orbit. Both of these problems have been solved previously (see 1,4,6,3]); here we present simple proofs and point out a connection between this problem and the analogous problem for nilpotent matrices. |
