Get RQ decomposition of concatenated matrices from the single RQ decompositions

I have a question: the subspace algorithms are based on the L-Q decomposition of a matrix. Suppose I have 2 matrices to be decomposed for example A1, A2. Is there a way in Matlab to get the decomposition of the matrix obtained by concatenating A1 A2 as

A =[A1, A2]

from the single decompositions?(Especially I am interested in the L matrix). I need this to concatenate the single channel models obtained to have a unique multi channel model of the same order.

If somebody knows a way to concatenate the SISO models obtained with n4sid function to get the multi channel model it would be even better. Thanks in advance

[Matt J]

You want the LQ decomposition? The title of your post says RQ.