Multiple alignment in align environment

Question

My MWE:

\documentclass[]{report}

\usepackage{amsmath}

    \begin{document}

    \begin{align}
    \dot{V} =&\, \frac{1}{\gamma_{2,1}}\sigma_{2,1} \dot{\sigma}_{2,1} + \frac{1}{\gamma_{2,2}}\sigma_{2,2} \dot{\sigma}_{2,2} + \frac{1}{\gamma_{2,3}}\sigma_{2,3} \dot{\sigma}_{2,3} \notag \\
     =& - \left [\sigma_{2,1}^2 \sin^2(x_1) + \sigma_{2,2}^2 x_2^2 + \sigma_{2,3}^2 u^2 + 2\sigma_{2,1}\sigma_{2,2}\sin(x_1)x_2 + 2 \sigma_{2,1}\sigma_{2,3}\sin(x_1)u \right. \notag \\
    & \left. + 2 \sigma_{2,2}\sigma_{2,3}x_2 u \vphantom{\sigma_{2,1}^2} \right ] \notag \\
    \end{align}

    \end{document}

The result:

What I want:

Answer 1

Use & \phantom{{}= - \bigl[}. Also, you should use &= instead of =&. Further, use \bigl[ and \bigr] instead of \left[ and right]. This doesn't need to be balanced like \left.. Also the \\ in the last line shouldn't be used. In the last line, use {}+{} so that the spacing around + is correct.

\documentclass[]{report}

\usepackage{amsmath}

\begin{document}

\begin{align}
\dot{V} &= \frac{1}{\gamma_{2,1}}\sigma_{2,1} \dot{σ}_{2,1} + \frac{1}{\gamma_{2,2}}\sigma_{2,2} \dot{σ}_{2,2} + \frac{1}{\gamma_{2,3}}\sigma_{2,3} \dot{σ}_{2,3} \notag \\
 &= {}-{} \bigl[\sigma_{2,1}^2 \sin^2(x_1) + \sigma_{2,2}^2 x_2^2 + \sigma_{2,3}^2 u^2 + 2\sigma_{2,1}\sigma_{2,2}\sin(x_1)x_2 + 2 \sigma_{2,1}\sigma_{2,3}\sin(x_1)u  \notag \\
& \phantom{{}= - \bigl[} {}+{} 2 \sigma_{2,2}\sigma_{2,3}x_2 u \vphantom{\sigma_{2,1}^2} \bigr] \notag   %% no \\ here
\end{align}

\end{document}

Here is another version with shorter second line as recommended by egreg.

\documentclass[]{report}

\usepackage{amsmath}

\begin{document}

\begin{align}
\dot{V} &= \frac{1}{\gamma_{2,1}}\sigma_{2,1} \dot{σ}_{2,1} + \frac{1}{\gamma_{2,2}}\sigma_{2,2} \dot{σ}_{2,2} + \frac{1}{\gamma_{2,3}}\sigma_{2,3} \dot{σ}_{2,3} \notag \\
 &= {}-{} \bigl[\sigma_{2,1}^2 \sin^2(x_1) + \sigma_{2,2}^2 x_2^2 + \sigma_{2,3}^2 u^2 + 2\sigma_{2,1}\sigma_{2,2}\sin(x_1)x_2  \notag \\
& \phantom{{}= - \bigl[} {}+{}  2 \sigma_{2,1}\sigma_{2,3}\sin(x_1)u + 2 \sigma_{2,2}\sigma_{2,3}x_2 u \vphantom{\sigma_{2,1}^2} \bigr] \notag   %% no \\ here
\end{align}

\end{document}