The given system in state space is of the form
x'=Ax+Bu
y=Cx+Du.
Note the typo on slide 15, where y should be [1 0 0 0]x.
Open MATLAB and store the matrices A, B, C, and D in four variables (say
a, b, c, d). Then say
>> InvPend=ss(a,b,c,d)
This command creates a state space model using the matrices stored
in a, b, c, and d (you need SIMULINK for this to work). Finally, say
>> bode(InvPend)
to get the BODE plot.