Details:
Title  Controlled invariant hypersurfaces of polynomial control systems.  Author(s)  Sebastian Walcher, Eva Zerz  Type  Article in Journal  Abstract  We study inputaffine 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.  Keywords  Inputaffine control systems, State feedback ,Invariant varieties, Syzygies  ISSN  15755460; 16623592/e 
URL 
http://link.springer.com/article/10.1007%2Fs1234601100487 
Language  English  Journal  Qual. Theory Dyn. Syst.  Volume  11  Number  1  Pages  145158  Publisher  Springer (Birkh\"auser), Basel  Year  2012  Edition  0  Translation 
No  Refereed 
No 
