# Obtaining state space from transfer functions

1. Nov 15, 2011

### Liferider

1. The problem statement
I have a MIMO system with two inputs and two outputs. I have all transfer functions between inputs and outputs. I want to obtain a state space model that describes this system. All transfer functions are of 3rd degree.

2. Relevant equations
"Transfer matrix":
HP(s)=[H11, H12; H21, H22]

H11=$\frac{1}{100s^3+80s^2+17s+1}$

H12=$\frac{0.5}{100s^3+80s^2+17s+1}$

H21=$\frac{4.8}{5s^3+13.5s^2+7.5s+1 }$

H22=$\frac{16}{5s^3+13.5s^2+7.5s+1 }$

Last edited: Nov 15, 2011
2. Nov 15, 2011

### Liferider

Solved it :-D

I created two equations for the outputs which resulted in two 3rd degree ODE's. From these two equations I created 6 states, where only two of them was of any interest to me, so I put those two states in the measurment equation of the state space model.