CONTINUITY PROPERTIES OF BALANCED REALIZATIONS

In this paper topological and geometrical properties of pre-balanced a nd balanced realizations are considered. It is shown that analytic pre -balancing coordinate transformations do exist and that the set of pre -balanced realizations forms an analytic submanifold. Explicit formula s for the tangent spaces and their dimension are derived. Continuity p roperties of balanced realizations are studied. For systems with more than two inputs and two outputs explicit points of discontinuity of ba lancing coordinate transformations are described. A certain class of b alancing coordinate transformations is shown to be discontinuous, even for distinct and fixed singular values. (C) 1998 Elsevier Science B.V . All rights reserved.