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400
200
0
−200
−400
−150
−100
−50
0
Real part
400
200
0
−200
−400
−150
−100
−50
0
Real part
Fig. 7 Poles distribution of FOM reduced switched system (order 10) with DRK-SLS method
frequency. The distribution poles in the complex plane of each subsystem is depicted
in Fig.
7
, all poles are negative real part, then the reduces switched linear subsystems
are stable.
3.1.2 Example 2: Simulation Results
In this part the largest singular value of the frequency response, the distribution
poles of the reduced switched system (BEAM order 24) and the absolute error
between original subsystem (BEAM order 348) and reduced one (BEAM order 24)
are presented.
The Fig.
8
presents the largest singular value of the frequency response of the
original switched linear system (Beam order 348) and reduced one (order 24) to a
frequency range by DRK-SLS method.
Note that when a correlation over the entire frequency range shape with a low
error rate for low frequency for the second subsystem. However for the
rst sub-
system, note that the correlation is not good.
The Fig.
9
shows the variation of the singular value of the absolute error between
the original switched linear system and the reduced one, note that the error is small
around the low frequency for the second subsystem, which is not the case for the
first subsystem. The distribution poles in the complex plane of each subsystem is
depicted in Fig.
10
, noting that the existence of positive real part poles, then the
reduces switched linear subsystems are unstable.
The use of the dual rational Krylov method does not guarantee the stability of the
reduced systems, so it does not minimise the error between the original subsystems
and the reduced ones over the entire frequency range. For these reasons, the iter-
ative dual rational Krylov method will be presented in the next section.
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