Product of two systems of linear differential equations

[Leo321]

I have two systems of linear differential equations: \frac{dx}{dt}=Ax, \frac{dy}{dt}=By
x,y are vectors of length n and A,B are nxn matrices.
I have a third system defined by: \frac{dz}{dt}=-ABz
Is there anything we can say about what the third system represents in terms of the first two?
If we know some things about the behavior of x and y, what could be useful ways of deducing something about z?

 

[Leo321]

Can z be expressed as a function of x,y?
Or is there some function so that z(t)<f(x(t),y(t))?
We can assume that x(t)>0,y(t)>0.

 

[Leo321]

Ok, I think I solved what I wanted through a different path. Thanks for the attempts, even if they were only at the mental level.