Creating and Manipulating Models

Multiplication

Multiplication of two LTI models connects them in series. Specifically,

• sys = sys1 * sys2
  

returns an LTI model sys for the series interconnection shown below.

Notice the reverse orders of sys1 and sys2 in the multiplication and block diagram. This is consistent with the way transfer matrices are combined in a series connection: if sys1 and sys2 have transfer matrices and , then

For state-space models sys1 and sys2 with data and , the state-space data associated with sys1*sys2 is

Finally, if sys1 is MIMO and sys2 is SISO, then sys1*sys2 or sys2*sys1 is interpreted as an entry-by-entry scalar multiplication and produces a system with the same dimensions as sys1, whose ijth entry is sys1(i,j)*sys2.

Addition and Subtraction

Inversion and Related Operations