\documentclass{book}
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\begin{document}

\begin{subequations}\label{E7}
\begin{equation}
\dot{x}^{(k)}(t)=Ax^{(k)}(t)+A_1x^{(k-1)}(t-\tau)+f(x^{(k-1)})-S\lambda^{(k)}(t)+Dv(t)
\end{equation}
\begin{align}
-\dot{\lambda}^{(k)}(t) =
\begin{cases}
Qx^{(k)}(t)+A^T\lambda^{(k)}(t)+f_x^T(x^{(k-1)})\lambda^{(k-1)}(t)+A_1^T\lambda^{(k-1)}(t-\tau)	   
&t_0\leq t\leq t_f-\tau\\
   Qx^{(k)}(t)+A^T\lambda^{(k)}(t)+f_x^T(x^{(k-1)})\lambda^{(k-1)}(t)
 & t_f-\tau\leq t\leq t_f\\
\end{cases}
\end{align}
\begin{equation}
x^{(k)}(t)=\phi(t)\qquad t_0 \leq t\leq t_f
\end{equation}
\begin{equation}
\lambda^{(k)}(t)=Q_fx^{(k)}(t_f)\qquad  t_0 \leq t\leq t_f
\end{equation}
\begin{equation}
x^{(0)}(t)\equiv 0,\qquad\lambda^{(0)}(t)\equiv 0, \qquad t_0 \leq t\leq t_f
\end{equation}
\end{subequations}

in(\ref{E7})

\end{document}