MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to understand a theorem about partial feedback linearization from the paper "On the largest feedback linearizable subsystem" by R. Marino (published in: Systems & Control Letters, Volume 6, Issue 5, Jan. 1986, pages 345-351).

My question concerns the proof of theorem 4. Citing:

Consider $\overline{G}^{\overline{k}^*_1-2}$. It is easy to see that there must exist an $(r_{k^*_1-1})$-vector function $\phi$, such that $$ d\phi_1 \subset (\overline{G}^{k^*_1-2})^{\bot} $$ and $$ \operatorname{rank} \langle d \phi_1, ad_f^{\overline{k}^*_1-1} G \rangle = r_{\overline{k}^*_1-1} $$

Is the first proposition a consequence of Frobenius' theorem? Where does the second proposition come from?

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.