Engineering domain: Control Design

Consider a nanopositioning stage modeled by the following seventh-order linear state-space system. This model is fitted to frequency response data collected from the physical device:
A = \begin{bmatrix}
-3360.27884342382 & 24650.4407238876 & -24650.4407238876 & 24650.4407238876 & -24650.4407238876 & 24650.4407238876 & -6162.61018097190 \\
-3270.26403683917 & 10278.7248098086 & -7476.39347226054 & 7476.39347226054 & -7476.39347226054 & 7476.39347226054 & -1869.09836806513 \\
-2657.10970968037 & 10628.4388387215 & -13430.7701762696 & 16233.1015138177 & -16233.1015138177 & 16233.1015138177 & -4058.27537845441 \\
-3954.03177459846 & 15816.1270983939 & -15816.1270983939 & 13013.7957608458 & -10211.4644232977 & 10211.4644232977 & -2552.86610582443 \\
-2325.45756017668 & 9301.83024070671 & -9301.83024070671 & 9301.83024070671 & -12104.1615782548 & 14906.4929158029 & -3726.62322895072 \\
-1665.81075466004 & 6663.24301864017 & -6663.24301864017 & 6663.24301864017 & -6663.24301864017 & 3860.91168109210 & -264.645085886005 \\
-1596.51916299641 & 6386.07665198562 & -6386.07665198562 & 6386.07665198562 & -6386.07665198562 & 6386.07665198562 & -4398.85050054448 \\
\end{bmatrix},
B = \begin{bmatrix}
33.1501 \\
29.2147 \\
49.7430 \\
55.4071 \\
43.2351 \\
22.8726 \\
24.9153 \\
\end{bmatrix},
C = \begin{bmatrix}
41.1585 & -164.6342 & 164.6342 & -164.6342 & 164.6342 & -164.6342 & 41.1585
\end{bmatrix}
D = \begin{bmatrix}
0
\end{bmatrix}.

Your task is to design a robust feedback controller using the loop shaping method that satisfies the following frequency-domain performance requirements:
-Closed-loop bandwidth: approximately 85 Hz (±10 Hz tolerance)
-Gain margin: greater than 1.5 dB
-Phase margin: greater than 60 degrees