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I want to form a MIMO state-space system from SIMO Transfer functions. Lets say that the system has 2 inputs (U1 and U2) and 2 states (X1 and X2).

If I apply U1 to the LTI system, I get X1 and X2 in a SIMO operation. And, I can extract 2 transfer functions: T11 (X1/U1) and T21 (X2/U1).

Similarly, if I apply U2 input, I can get T12 (X1/U2) and T22 (X2/U2).

So, I have 4 SISO transfer functions of the system.

I want to use them to generate a state space matrix of the system. How can I do that?

Thanks in advance.

shadowfax
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In general, there are infinitely many choices for state-space representations of your matrix transfer function (T). It is sensible to choose the one with lowest order (smallest number of states) often called the "minimal realization."

There are many approaches to computing the minimal realization. Some are algorithmic starting with T and arriving at the minimal A*,B*,C*,D* immediately. Others suppose that you already found some non-minimal A,B,C,D by inspection, and then provide the procedure for transforming that non-minimal representation into the minimal one.Typically it is a matrix transformation of A and B into some canonical form that exposes uncontrollable (sometimes called "unreachable") states.

http://www.egr.msu.edu/classes/me851/jchoi/lecture/Lect_20.pdf

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-241j-dynamic-systems-and-control-spring-2011/readings/MIT6_241JS11_chap25.pdf

https://www.youtube.com/watch?v=cnbY2AUtGAY&t=2m14s

If you are less concerned with manual implementation, in MatLab use the function tf2ss.

jnez71
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