Creating and Manipulating Models

Dimensions, Size, and Shape of an LTI Array

The dimensions and size of a single LTI model are determined by the output and input channels. An array of LTI models has additional quantities that determine its dimensions, size, and shape.

There are two sets of dimensions associated with LTI arrays:

• The I/O dimensions--the output dimension and input dimension common to all models in the LTI array
• The array dimensions--the dimensions of the array of models itself

The size of the LTI array is determined by:

• The lengths of the I/O dimensions--the number of outputs (or inputs) common to all models in the LTI array
• The length of each array dimension--the number of models along that array dimension

The next figure illustrates the concepts of dimension and size for the LTI array m2d, a 2-by-3 array of one-input, two-output transfer function models.

Figure 4-5: Dimensions and Size of m2d, an LTI Array

You can load this sample LTI array into your workspace by typing

• load LTIexamples
  size(m2d)
  2x3 array of continuous-time transfer functions
  Each transfer function has 2 outputs and 1 input.
  

The I/O dimensions correspond to the row and column dimensions of the transfer matrix. The two I/O dimensions are both of length 1 for SISO models. For MIMO models the lengths of these dimensions are given by the number of outputs and inputs of the model.

Five related quantities are pertinent to understanding the array dimensions:

• N, the number of models in the LTI array
• K, the number of array dimensions
• , the list of lengths of the array dimensions
• is the number of models along the dimension.
• , the configuration of the models in the array
• The configuration determines the shape of the array.
• The product of these integers is N.

In the example model m2d,:

• The length of the output dimension, the first I/O dimension, is 2, since there are two output channels in each model.
• The length of the input dimension, the second I/O dimension, is 1, since there is only one input channel in each model.
• N, the number of models in the LTI array, is 6.
• K, the number of array dimensions, is 2.
• The array dimension lengths are [2 3].
• The array configuration is 2-by-3.

Higher Dimensional Arrays of LTI Models

size and ndims