Specifications

2 LTI Models
2-44
•Interconnections of continuous-time delay systems as long as the resulting
transfer function from input to output is of the form
where is a rational function of
•Padé approximation of time delays (
pade)
Specifying Input/Output Delays
Using the ioDelay property, you can specify frequency-domain models with
independent delays in each entry of the transfer function. In continuous time,
such models have a transfer function of the form
where the ’s are rational functions of , and is the time delay between
input and output . See “Specifying Delays inDiscrete-Time Models” on page
2-50 for details on the discrete-time counterpart. We collectively refer to the
scalars as the I/O delays.
The syntax to create above is
H = tf(num,den,'ioDelay',Tau)
or
H = zpk(z,p,k,'ioDelay',Tau)
where
•
num, den (respectively,z, p, k) specify the rational part ofthe transfer
function
•
Tau is the matrix of time delays for each I/O pair. That is, Tau(i,j) specifies
the I/O delay in seconds. Note that
Tau and should have the same
row and column dimensions.
You can also use the
ioDelay property in conjunction with state-space models,
as in
sys = ss(A,B,C,D,'ioDelay',Tau)
j
is
τ
ij
–
()
h
ij
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exp
h
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s
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e
s
τ
11
–
h
11
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()
... e
s
τ
1m
–
h
1m
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()
::
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s
τ
p1
–
h
p1
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()
... e
s
τ
pm
–
h
pm
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()
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τ
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–
()
h
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exp
[]
==
h
ij
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τ
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j
i
τ
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()
h
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Hs
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τ
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()