User`s guide

Operations on LTI Models
1-11
Operations on LTI Models
You can perform simple matrix operations, such as addition, multiplication, or
concatenation on LTI models. See C hapter 3, “Operations on LTI M odels” for
more information. Thanks to MATLAB object-oriented programming
capabilities, these operations assume appropriatefunctionalities when applied
to LTI models. For example, addition performs a parallel interconnection. Type
tf(1,[1 0]) + tf([1 1],[1 2])% 1/s + (s+1)/(s+2)
and MATLAB responds:
Transfer function
s^2 + 2 s + 2
-------------
s^2 + 2 s
Multiplication performs a series interconnection. Type
2 * tf(1,[1 0])*tf([1 1],[1 2])% 2*1/s*(s+1)/(s+2)
and MATLAB responds
Transfer function:
2 s + 2
---------
s^2 + 2 s
If the operands are models of different types, t he resulting model t ype is
determined by precedence rules; see “Precedence Rules” on page 2-5 for more
information. State-space models have highest precedence while transfer
functions have lowest precedence. Hence the sum of a transfer function and a
state-space model is always a state-space model.
Other available operations include system inversion, transposition, and
pertransposition; see “Inversion and Related Operations” on page 3-13.
Matrix-like indexing for extracting subsystems is also supported; see
“Extracting and Modifying Subsystems” on page 3-5 for more information. For
instance, if
sys is a MIMO system with two inputs and three outputs,
sys(3,1)