Combine ARX models - System Identification Toolbox

Hello, how are you doing?

I have the following problem: I am using MATLAB's System Identification Toolbox to model a MISO (Multiple-Input Single-Output) system based on different intervals. let us assume that we have three intervals of data: I1, I2 and I3, and that our system is a 3x1 system. With each interval, I will be obtaining a model for the single output using one of the 3 inputs, as bellow:

Y_1 = G11(z)U1(z)
Y_2 = G21(z)U2(z)
Y_3 = G31(z)U3(z)

What I want to do next is to add these models to obtain a single MISO model:

Y(z) = Y_1(z)+Y_2(z)+Y_3(z) = 
Y(z) = G11(z)U1(z) + G21(z)U2(z) + G31(z)U3(z)

I am using a ARX structures to do that, with a validation set Zv:

NN = struc(1:30 ,1:30 ,1:30);

N1 = selstruc(arxstruc(Ze1(:,:,1),Zv(:,:,1),NN));
arx1 = arx(Ze1, "na", N1(1), "nb", [N1(2) 0 0], "nk", [N1(3) 1 1]);
 
N2 = selstruc(arxstruc(Ze2(:,:,2),Zv(:,:,2),NN));
arx2 = arx(Ze2, "na", N2(1), "nb", [0 N2(2) 0], "nk", [1 N2(3) 1]);
 
N3 = selstruc(arxstruc(Ze3(:,:,3),Zv(:,:,3),NN));
arx3 = arx(Ze3, "na", N3(1), "nb", [0 0 N3(2)], "nk", [1 1 N3(3)]);

The problem:

If I make ARX = arx1+arx2+arx, I end up with a state-space system that loses the noise properties of the ARX system. Therefore, if I make

compare(Zv,ARX2,inf) -> infinity steps-ahead

or

compare(Zv,ARX2,1) -> 1 step-ahead

the result is the same, beacause "compare ignores kstep when sys is an iddata object, an FRD model, or a dynamic system with no noise component".

What I wanna know:

1) When using compare, in this case, how many steps it is actually using?

2) How can I add the 3 ARX systems and make both the 1 step-ahead and the infinity step-ahead validations?

I really appreciate any help!

Best regards,

[Rajiv Singh]

Is this question same as one answered in:

https://www.mathworks.com/matlabcentral/answers/539675-why-cant-i-predict-kstep-ahead-when-adding-system-identification-models