Canonical forms for bilinear input/output maps

In an earlier paper [1], necessary and sufficient conditions were obtained for a state-space realization of a bilinear inout/output map to be quasi-reachable and observable, and procedures were introduced for reducing any realization not of this type to one which is. In rids paper, it is shown that any two such quasi-reachable and observable (or canonical) realizations are isomorphic, and using this result, it is possible to generate canonical forms for these realizations by means of complete sets of independent invariants.