𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Continuity properties of balanced realizations

✍ Scribed by G. Dirr; U. Helmke

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
105 KB
Volume
34
Category
Article
ISSN
0167-6911

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper topological and geometrical properties of pre-balanced and 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 formulas for the tangent spaces and their dimension are derived. Continuity properties of balanced realizations are studied. For systems with more than two inputs and two outputs explicit points of discontinuity of balancing coordinate transformations are described. A certain class of balancing coordinate transformations is shown to be discontinuous, even for distinct and ΓΏxed singular values.

πŸ“œ SIMILAR VOLUMES

On the stability of projections of balan
On the stability of projections of balanced realizations
✍ James Lam; Y.S. Hung πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 683 KB

This paper generalizes a stability property concerning the state matrix of a balanced realization established by Pernebo and Silverman. It is shown that stability is preserved under a general projection of the state matrix provided that the Hankel singular values of the realization are distinct. A n

On the bilinear transformation of LQG-ba
On the bilinear transformation of LQG-balanced realizations
✍ L. Fortuna; G. Muscato; G. Nunnari πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 313 KB

## This contribution shows that some useful properties of LQG-balanced realizations of continuous-time systems are preserved by applying bilinear transformations. This fact suggests that LQG-balancing of discrete systems and its approximation can be performed by using the typical schemes successfu

Closed-loop balanced realizations of LTI
Closed-loop balanced realizations of LTI discrete-time systems
✍ L. Fortuna; G. Muscato; G. Nunnari πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 624 KB

The problem of closed-loop baIancing discrete LTI models is addressed. It is shown that results similar to those known for the continuous case can be extended to the discrete case. A new cross-Riccati equation is introduced which allows the direct balancing of MIMO symmetric discrete systems avoidin

On the nonuniqueness of singular value f
On the nonuniqueness of singular value functions and balanced nonlinear realizations
✍ W.Steven Gray; Jacquelien M.A. Scherpen πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 374 KB

The notion of balanced realizations for nonlinear state space model reduction problems was ΓΏrst introduced by Scherpen in 1993. Analogous to the linear case, the so-called singular value functions of a system describe the relative importance of each state component from an input-output point of view