The main contributions are summarized as follows:
\begin{itemize}
\item [1)]
To the best of our knowledge,this is the first time that the function proposed in this paper to deal with asymmetric input constraints, and the symmetric input constraints are also considered by changing the function.
\item [2)]
Considering the inaccuracy of nonlinear continuous system modeling or external interference,the $H_{\infty}$ control problem is transformed into a zero sum game problem, and the optimal control law and the worst disturbance law are obtained by solving the HJI equation.
\item [3)]
\end{itemize}
