State Space Differential Equation HW

[kev08106]

Hi I have a problem I need to solve for a class soon.
The prof gave a us a homework problem where he gives us a state space representation for one system and connect it in cascade to another system and need the equivalent state space parameters: I'm pretty confused.
Heres the question:
x(t)----> |system1 | --> y(t) --> |system2 |----> z(t)

system 1 is defined by:
dq1(t)/dt = A1(t)q1(t) + B1(t)x(t)
y(t) = C1(t)q1(t)

system 2 is defined by:
dq2(t)/dt = A2(t)q2(t) + B2(2)y(t)
z(t) = C2(t)q2(t)

the combination of the system is defined:
dq(t)/dt = A(t)q(t) + B(t)x(t)
z(t) = C(t)q(t)

It says find q(t), A(t), B(t), and C(t) in similar quantities for the separate systems.

 

[lippyka]

Can someone please help me understand this problem better? I'm really lost. Thank you!Here is one way of solving the problem:Let q(t) = [q1(t),q2(t)] and A(t) = [[A1(t), 0], [B2(t)*C1(t), A2(t)]]B(t) = [B1(t), 0]C(t) = [C1(t), C2(t)]Then the combined system can be written as:dq(t)/dt = A(t)q(t) + B(t)x(t)z(t) = C(t)q(t)This is the equivalent state space representation for the combined system.