Specifications

5 Arrays of LTI Models
5-16
When you concatenate several models or LTI arrays along the jth array
dimension, such as in
stack(j,sys1,sys2,...,sysn)
•The lengths of the I/O dimensions of sys1,...,sysn must all match.
•The lengths of all but the jth array dimensionof
sys1,...,sysn must match.
For example, if two TF models
sys1 and sys2 have the same number of inputs
and outputs,
sys = stack(1,sys1,sys2)
concatenates them into a 2-by-1 array of models.
There are two principles that you should keep in mind:
•
stack only concatenates along an array dimension, not an I/O dimension.
•To concatenate LTI models or LTI arrays along an input or output
dimension, use the bracket notation (
[,] [;]). See “Model Interconnection
Functions” for more information on the use of bracket notation to
concatenate models. See also “Special Cases for Operations on LTI Arrays”
for some examples of this type of concatenation of LTI arrays.
Here’s an example of how to build the LTI array
H using the function stack.
% Set up the parameter vectors.
zeta = [0.66,0.75];
w = [1.2,1.5];
% Specify the four individual models with those parameters.
%
H11 = tf(w(1)^2,[1 2*zeta(1)*w(1) w(1)^2]);
H12 = tf(w(2)^2,[1 2*zeta(1)*w(2) w(2)^2]);
H21 = tf(w(1)^2,[1 2*zeta(2)*w(1) w(1)^2]);
H22 = tf(w(2)^2,[1 2*zeta(2)*w(2) w(2)^2]);
% Set up the LTI array using stack.
COL1 = stack(1,H11,H21); % The first column of the 2-by-2 array
COL2 = stack(1,H12,H22); % The second column of the 2-by-2 array
H = stack(2, COL1, COL2); % Concatenate the two columns of models.