Abstract
In this paper 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 multivariable case a noncontrollable system may lie in the boundary of finitely or even infinitely many equivalence classes.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
