Do you prefer this type of bold big braces or more bigger than \Bigg? Here there is a minimal working example with a specific screenshot.

%% Compile and read me!
\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{bm}
\SetSymbolFont{largesymbols}{bold}{OMX}{txex}{b}{n} %%%% >--- see the link https://latex.org/forum/viewtopic.php?t=27058
\begin{document}
\begin{equation}
x_k = \bm{\Bigg[}\begin{matrix} 1 & T_s & \frac{T_s^2}{2} \\ 0 & 1 & T_{s} \\ 0 & 0 & 1\end{matrix}\bm{\Bigg]} x_{k-1} + \xi
\end{equation}
\end{document}
If you use scalerel package created by @Steven B. Segletes with the option scaleobj you can obtain:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{bm}
\usepackage{scalerel}
\SetSymbolFont{largesymbols}{bold}{OMX}{txex}{b}{n}
\begin{document}
\begin{equation}
x_k = \scaleobj{1.2}{\bm{\Bigg[}}\begin{matrix} 1 & T_s & T_s^2/2 \\ 0 & 1 & T_{s} \\ 0 & 0 & 1\end{matrix}\scaleobj{1.2}{\bm{\Bigg]}}\,x_{k-1} + \xi
\end{equation}
\end{document}