How to Derive the Output Equation from State-Space Models?

[rAz:DD]

Hello.
I have some trouble solving this exercise.

For this given linear system:

with the input Tm(T)
described by these equations

or re-written this way

It's also suggested that the states should be considered this way

resulting

I have to find out the state-space model (A,B,C,D matrix).

How do i find the output (y) equation ?
y is supposed to be a 2x1 matrix, with both theta L and theta M as outputs.

I tried solving this by calculating the transfer matrix of the system, but it seems that the denominator has 4 poles, but the number of states is 3. How should the size of A be?
The thing that bugs me is that the first state (x1) is a difference between those two variables i don't know. For the other exercises, the output was usually one of the states, so i was easy finding out its equation.

 

[nilesh_pat]

Any help would be greatly appreciated. Thanks in advance.The output equation can be determined by using the state equations and the input equation. For example, for the first state equation with input Tm(t):x1' = [Tm(t) + theta_L - theta_M]/JThis equation can be rearranged to solve for theta_L:theta_L = x1' J + Tm(t) + theta_MFrom this equation, the output variable theta_L can be expressed in terms of the state variable x1 and the input Tm(t). The same process can be repeated for the other state equations and the other output variable theta_M. Once the output variables are expressed in terms of the state variables and the input, the matrices A, B, C, and D can be determined.