To get rid of the error message generated by the caption, change _ to \_ in the argument of \caption.
You also should contemplate fixing several other issues. Do get rid of the font size changes within the formula, the \hline directive, and the changes to \arraystretch. Use \dfrac instead of \frac if you want larger fraction terms.

\documentclass{article}
\usepackage[italian]{babel}
\usepackage{amsmath} % for 'bmatrix' environment and '\dfrac' macro
\usepackage[a4paper,margin=2.5cm]{geometry} % set page and text block parameters
\begin{document}
\begin{table}
\[
\begin{bmatrix} y_\triangle \\ y \end{bmatrix}
%%%\Large
=
%%%\renewcommand\arraystretch{2}
\begin{bmatrix}%%%[c|ccc]
-\dfrac{\omega_i C C_{\mathrm{dyn}} H G}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_i C C_{\mathrm{dyn}}}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_i}{1+C C_{\mathrm{dyn}} H G} &
-\dfrac{\omega_i C C_{\mathrm{dyn}} H}{1+C C_{\mathrm{dyn}} H G} \\[3ex] %%%\hline
\dfrac{\omega_p G}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_p C C_{\mathrm{dyn}} G}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_p G}{1+C C_{\mathrm{dyn}} H G} &
-\dfrac{\omega_p C C_{\mathrm{dyn}} H G}{1+C C_{\mathrm{dyn}} H G}
\end{bmatrix}
%%%\normalsize
%%%\renewcommand\arraystretch{1}
\begin{bmatrix} u_\triangle \\ r\\ \omega \\ n \end{bmatrix}
\]
\caption{Trasformata U\_LFT del sistema} % <--- change "_" to "\_"
\label{fig:ulft}
\end{table}
\end{document}
Addendum: If you must insert a vertical and a horizontal line in the 2x4 matrix, I suggest you do so by using an array environment, rather than a bmatrix environment. That way, you won't have \hline generating a line that's too long and ends up interfering with the square brackets.
\left[ \begin{array}{@{}c|ccc@{}}
-\dfrac{\omega_i C C_{\mathrm{dyn}} H G}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_i C C_{\mathrm{dyn}}}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_i}{1+C C_{\mathrm{dyn}} H G} &
- \dfrac{\omega_i C C_{\mathrm{dyn}} H}{1+C C_{\mathrm{dyn}} H G} \\[2ex]
\hline
% use '\mathstrut' to get a bit more vertical separation:
\dfrac{\omega_p G^{\mathstrut}}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_p C C_{\mathrm{dyn}} G}{1+C C_{\mathrm{dyn}} H G} &
\dfrac{\omega_p G}{1+C C_{\mathrm{dyn}} H G} &
- \dfrac{\omega_p C C_{\mathrm{dyn}} H G}{1+C C_{\mathrm{dyn}} H G}
\end{array}\right]
\begin{bmatrix}[c|ccc]can't be correct. Did you mean to write\left[ \begin{array}{c|ccc}instead -- and\end{array}\right]instead of\end{bmatrix}? What, incidentally, is the (mathematical) purpose of the vertical line, as well as of the\hlinedirective that's in your code? – Mico Jan 23 '17 at 11:34\renewcommand*\env@matrixcode to your preamble, to see that[c|ccc]works, – Torbjørn T. Jan 23 '17 at 11:45\renewcommand*\env@matrixcode; I had completely missed it. That said, the\hlinethat's generated by the OP's code is much too long. – Mico Jan 23 '17 at 12:03arrayenvironment. – Mico Jan 23 '17 at 12:15