Specifications

2 LTI Models
2-48
Specifying Delays on the Inputs or Outputs
Whileidealforfrequency-domainmodelswithI/Odelays,the ioDelay property
is inadequate to capture delayed inputs or outputs in state-space models. For
example, the two models
share the same transfer function
As a result, they cannot be distinguished using the
ioDelay property (the I/O
delay value is 0.1 seconds in both cases). Yet, these two models have different
state trajectories since and are related by
Note that the 0.1 second delay is on the input in the first model, and on the
output in the second model.
InputDelay and OutputDelay Properties
When the state trajectory is of interest, you should use the InputDelay and
OutputDelay
properties to distinguish between delays on the inputs and
delays on the outputs in state-space models. For example, you can accurately
specify the two models above by
M1 = ss(–1,1,1,0,'inputdelay',0.1)
M2 = ss(–1,1,1,0,'outputdelay',0.1)
In the MIMO case, you can specify a different delay for each input (or output)
channel by assigning a vector value to
InputDelay (or OutputDelay).For
example,
sys = ss(A,[B1 B2],[C1;C2],[D11 D12;D21 D22])
sys.inputdelay = [0.1 0]
sys.outputdelay = [0.2 0.3]
creates the two-input, two-output model
M
1
()
x
·
t
()
x– t
()
ut 0.1–
()
+=
yt
()
xt
()
=
è


M
2
()
z
·
t
()
z– t
()
ut
()
+=
yt
()
zt 0.1–
()
=
è


hs
()
e
0.1s–
s 1+
----------------
=
xt
()
zt
()
zt
()
xt 0.1–
()
=