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Fig. 8.18
Building automation system software architecture
systems described by time-delay members only (Lewoc et al.
2010b
). The formulae
for the basic robustness value, the Doyle's
μ
function, are given by Eqs. (
8.1
) and
(
8.2
), with:
s
: index of the star configuration
r
: index of the ring (common medium) configuration
ʔ: small perturbation
G
: transfer matrix
ω
: frequency
t
i
: time delay limitation
˄
i
: time delays
T
i
: time delay components
The formulae are fairly simple, facilitating efficient evaluation of the robustness
measures:
(
)
(
)
(
)
(
)
()
m
G in 21
=
−
cos
w
t
−
t
:
det1G0
+
D
=
(8.1)
S
i
i
S
i
=1,..,
n
i
w
w
(
D
)
()
∑
m
G in 21
=
−
cos
t
−
T
:
det1 G
+
=
0
(8.2)
R
i
m
R
i
i
=
1,..,
n
m
=
1
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