Creating and Manipulating Models

Viewing LTI Systems As Matrices

In the frequency domain, an LTI system is represented by the linear input/output map

This map is characterized by its transfer matrix H, a function of either the Laplace or Z-transform variable. The transfer matrix H maps inputs to outputs, so there are as many columns as inputs and as many rows as outputs.

If you think of LTI systems in terms of (transfer) matrices, certain basic operations on LTI systems are naturally expressed with a matrix-like syntax. For example, the parallel connection of two LTI systems sys1 and sys2 can be expressed as

• sys = sys1 + sys2
  

because parallel connection amounts to adding the transfer matrices. Similarly, subsystems of a given LTI model sys can be extracted using matrix-like subscripting. For instance,

• sys(3,1:2)
  

provides the I/O relation between the first two inputs (column indices) and the third output (row index), which is consistent with

for .

Precedence Rules

Command Summary