Partial feedback linearization (Control theory) - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T21:46:47Z http://mathoverflow.net/feeds/question/83352 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83352/partial-feedback-linearization-control-theory Partial feedback linearization (Control theory) Ash Shevlyakov 2011-12-13T17:06:21Z 2011-12-18T09:41:48Z <p>Greetings, I'm trying to understand a theorem about partial feedback linearization from a paper "On the largest feedback linearizable subsystem" by R.Marino (you can find it here: <a href="http://www.mediafire.com/?si2t4lnhxa4jt82" rel="nofollow">http://www.mediafire.com/?si2t4lnhxa4jt82</a>)</p> <p>My question is concerning proof of theorem 4. Citing:</p> <p>Consider <code>$\overline{G}^{\overline{k}^*_1-2}$</code>. It is easy to see that there must exist an <code>$(r_{k^*_1-1})$</code>-vector function $\phi$, such that <code>$$d\phi_1 \subset (\overline{G}^{k^*_1-2})^{\bot}$$</code> and <code>$$rank &lt;d \phi_1, ad _f^{\overline{k}^*_1-1} G&gt;=r_{\overline{k}^*_1-1}$$</code></p> <p>Is the first proposition a consequence of Frobenius theorem? Where does the second proposition come from?</p>