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TitleControlled invariant hypersurfaces of polynomial control systems.
Author(s) Sebastian Walcher, Eva Zerz
TypeArticle in Journal
AbstractWe study input-affine control systems with polynomial nonlinearity. A variety V is said to be controlled invariant if there exists a feedback law of polynomial type that causes the closed loop system to have V as an invariant variety. Using the theory of Gröbner bases, we show how to constructively decide whether a given variety is controlled invariant for a given system, and if so, how to determine all feedback laws achieving the task. We also describe a set of “trivial” vector fields for which V is invariant. If V is a smooth hypersurface, then V is only invariant for its trivial vector fields. We discuss conditions under which the converse is also true.
KeywordsInput-affine control systems, State feedback ,Invariant varieties, Syzygies
ISSN1575-5460; 1662-3592/e
URL http://link.springer.com/article/10.1007%2Fs12346-011-0048-7
JournalQual. Theory Dyn. Syst.
PublisherSpringer (Birkh\"auser), Basel
Translation No
Refereed No