State space representations for different system configurations

[ChiaT]

Homework Statement

Homework Equations

This is the problem that I am trying to solve.

The Attempt at a Solution

https://docs.google.com/file/d/0B0Wxm870SWTNV0xjdmVRc09TTm8/edit

The approach of solving this problem is to first convert the two systems' state space representations into s-domain, combine them, then finally convert the final result back to the frequency domain. I am stuck; I can find the output, y, but I don't know how do I derive the state representation from the output. Is my approach correct? or do I need to use another approach? Any suggestion will be appreciated; thank you in advance!

 

[KataKoniK]

Thank you for sharing your problem and approach with us. It seems like you are on the right track by converting the systems into s-domain and combining them. However, in order to derive the state representation from the output, you will need to use the inverse Laplace transform. This will allow you to convert the combined s-domain representation back to the time domain, where you can then manipulate the equations to solve for the state variables.

Another approach you could consider is using the transfer function of each system to determine the overall transfer function for the combined system. This would involve multiplying the transfer functions together and then converting the result back to the time domain using the inverse Laplace transform.

I hope this helps and good luck with your problem solving! If you have any further questions, please don't hesitate to ask.