Two-Link Inverted Pendulum: Parameter Change and Response

I faced big trouble..
Any kind of help or comment will be welcoming...^^;;

Think about 2-link inverted pendulum consisting of A(top link) and B(bottom link).
Both links are connected with pin joint and bottom link also fixed at the ground with pin joint.
This inverted pendulum is controlled by PD controller (feedback gain : 2X4 matrix).

ok, gain matrix is determined, which means control strategy is fixed in any how..

There are some constraints. "total mass and total length should be always same."
in other words,
[1] mass of A + mass of B = const. , but mass ratio(mass of A/mass of B) changes..
[2] length of each link does not change. always the same.
of course, moment of inertia of each link will be changed as depending on mass change..

In this case(same feedback gain & two constraints), when perturbation is applied to the system,
system response(angle of A and B) and control inputs(torque of A and B) may be changed depending on the parameter(mass ratio) change..

Can I predict how system response and control input change with the change of the mass ratio of inverted pendulum?
yeah, I am now simulating inverted pendulum with MATLAB, but i want analytical way... by hand.
This is not one-segment, but multi-segment inverted pendulum..2 degree of freedom..
It's really hard to solve the eigenvalue problem or etc... by hand.

I want to explain the relationship between "parameter ratio change" and "system response"..
Is it possible to solve and demonstrate by hand ?

thanks in advance..