Can the u part of the matrix be written differently in state space analysis?

[phiby]

I posted this question in the engineering section, but didn't get any replies there - hence posting it here.

Below is a screen shot from state space analysis in "Control Engineering" by Ogata.

http://www.flickr.com/photos/66943862@N06/6230432028/"

I am trying to get at Eqn 3-20 from Eqn 3-18.

Can't the u part of the matrix also be written as
[1/m 0]^T instead of [0 1/m]^T?

What's the rationale in choosing one over the other?

 

[Fredrik]

I posted this question in the engineering section, but didn't get any replies there - hence posting it here.

Below is a screen shot from state space analysis in "Control Engineering" by Ogata.

http://www.flickr.com/photos/66943862@N06/6230432028/"

I am trying to get at Eqn 3-20 from Eqn 3-18.

Can't the u part of the matrix also be written as
[1/m 0]^T instead of [0 1/m]^T?

What's the rationale in choosing one over the other?

It can, but only if you swap the first and the second row in all the other matrices as well. If you only do it to the last term as you suggest, then if you perform the matrix multiplication and matrix addition on the right-hand side of (3-20) you get two equations that are similar to (3-17) and (3-18) but have the term involving u in the one that looks like (3-17) instead of in the one that looks like (3-18).

 

[phiby]

It can, but only if you swap the first and the second row in all the other matrices as well. If you only do it to the last term as you suggest, then if you perform the matrix multiplication and matrix addition on the right-hand side of (3-20) you get two equations that are similar to (3-17) and (3-18) but have the term involving u in the one that looks like (3-17) instead of in the one that looks like (3-18).

Yes, true. Stupid of me not to see that. Thank you.