\documentclass{article}
\usepackage{placeins}
\begin{document}
\tableofcontents
\newpage
\section{Introduction}
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\makeatletter \@addtoreset{figure}{section} \makeatother
\begin{figure} [H]
\caption{description of figure }
\end{figure}
\begin{figure}[H]
\caption{description of figure }
\end{figure}
\FloatBarrier
\section{Results}
\renewcommand\thefigure{\arabic{section}.\arabic{f igure}}
\makeatletter \@addtoreset{figure}{section} \makeatother
\begin{figure} [H]
\caption{description of figure }
\end{figure}
\FloatBarrier
\appendix
\section{Appendix}
\subsection{Additional figures}
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\makeatletter \@addtoreset{figure}{section} \makeatother
\begin{figure} [H]
\caption{appendix-figure}
\end{figure}
\FloatBarrier
\subsection{List of figures}
\listoffigures
\end{document}
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