Hinrichsen, Diederich; O’Halloran, J. A complete characterization of orbit closures of controllable singular systems under restricted system equivalence. (English) Zbl 0701.93017 SIAM J. Control Optimization 28, No. 3, 602-623 (1990). Summary: Properties of the orbit space of controllable generalized state-space systems modulo restricted system equivalence are derived. In particular, it is shown that this space is a smooth quasiprojective variety of dimension nm. Then the possible degenerations of controllable systems under transformations of restricted system equivalence are characterized and it is proved that every noncontrollable system can be approximated by a family of controllable systems that belong to a single equivalence class. In the single input case, this class is uniquely determined, whereas in the multivarible case a noncontrollable system may lie in the boundary of finitely or even infinitely many equivalence classes. Cited in 8 Documents MSC: 93B27 Geometric methods 14D20 Algebraic moduli problems, moduli of vector bundles Keywords:singuar system; restricted system equivalence; pencils; algebraic group actions; orbit spaces; orbit closures; controllable generalized state- space systems; smooth quasiprojective variety PDFBibTeX XMLCite \textit{D. Hinrichsen} and \textit{J. O'Halloran}, SIAM J. Control Optim. 28, No. 3, 602--623 (1990; Zbl 0701.93017) Full Text: DOI