Simulation of a nonlinear system in MATLAB

I have a nonlinear model that is represented by: TVo/V*X''+X'=KVo/V*D
where D is the control input. I wanted to design an integral
controller to control X to some Xd(desired) Assuming that V=Vo. I did
that with no problem. Next, I wanted to design a gain scheduling to
compensate for slowly varying V. I did that as well.

Now I have to simulate the system performance with MATLAB using both
controllers to a square wave input in which Xd varies between X1 and
X2 while slowing varying V. I'm not sure about the square input part,
I don't quite understand what and how to do it. I might be missing
something here.

If it helps I will explain how I found the design for the integral
controller:
Integral control: I did change of variables so that Y1=X, Y2=Y1'=X'
Y1'= Y2, Y2'=KD/T-Y2/T
X-Xr=e=W' (error which at steady state becomes zero b/c of the
integral controller).
D=-K1Y1-K2Y2-K3W (Assuming linear PI controller). After linearing the
system, I ended up with 2 state spaces that represent Y1-Y1ss, Y2-Y2ss
& W-Wss (where ss represents steady state).

[ Y1-Y1ss;Y2-Y2ss;W-Wss]' = [0 1 0;-K*K1/T  (-1-K*K2)/T -K*K3/T;1 0
0]* [Y1-Y1ss;Y2-Y2ss;W-Wss]

All of K,K1,K2,K3 & T have to be chosen so that the matrix is
hurwitz.

 Any explanation or help would be appreciated. Thanks.