Minimum norm regularization of descriptor systems by mixed output feedback
✍ Scribed by Delin Chu; Volker Mehrmann; Nancy K. Nichols
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 244 KB
- Volume
- 296
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
We study the regularization problem for linear, constant coecient descriptor systems i
x ex fuY y 1 gxY y 2 C x by proportional and derivative mixed output feedback. Necessary and sucient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and i fqC has a desired rank, i.e., there is a desired number of dierential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.