deletions | additions       diff --git a/Stability and Convergence Proof.tex b/Stability and Convergence Proof.tex  index 4198750..0d94d77 100644  --- a/Stability and Convergence Proof.tex  +++ b/Stability and Convergence Proof.tex 
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\section{System analysis}  relative degree 1 order of $G_nm = n$  A transfer function loses its controllability or observability through zero-pole-cancelation \cite{lunze2}.   \begin{align}  F(s) = \frac{1}{\lambda(s)}[1,s,\ldots,s^{n-2}]^T  \\\lambda(s) = a_{n-1}s^{n-1} + a_{n-2}  \end{align}  Therefore it is necessary but not sufficient that the zeros of the transfer function $F(s) = \frac{1}{\lambda(s)}[1,s,\ldots,s^{n-2}]^T$ don't cancel out the roots. The only possible case in which a zero-pole-cancellation occurs is for   F is controllable due to the fact that