Set of SISO transfer functions to MIMO transfer function

I have a set of transfer functions showing individual interactions between two inputs and two outputs of a MIMO system - in other words, I have SISO equations showing interactions between the controlled variables and the manipulated variables. As an example:

Now I want to have the overall system equation of the MIMO system. How do I do that? Intuitively, I think the MIMO system equation should be and, .

However, I am little confused. Thanks for your help in advance.

[Dhanashree Mohite]

Does it mean, how to get MIMO Transfer function using multiple SISO Transfer function in MATLAB?

[Jilan Samiuddin]

Yes, that is what I mean. Provided the 4 SISO transfer functions for 2-inputs-2-outputs system, I want the MIMO transfer function.

Answer 1

[Dhanashree Mohite]

As you want to create Transfer function model in MATLAB, you can use ‘tf’ function.

For your case it will be:

Numerator = {1,2 ; 50,300};
Denominator = {[10 1],[16 1] ; [300 30 1], [20 1]};
H = tf(Numerator,Denominator,'InputName',{'u1' 'u2'},...
        'OutputName',{'y1' 'y2'},...
        'Variable','s');

Please refer below link for more understanding:

https://www.mathworks.com/help/control/ref/tf.html?s_tid=doc_ta