Iterative Dual Rational Krylov and Iterative SVD-Dual Rational Krylov Model Reduction for Switched Linear Systems - Complex System Modelling and Control Through Intelligent Soft Computations - page 422

5.1 Numerical Example

To evaluate this approach the same model used previously is taken with the same
switching signal. Given the largest singular value of the frequency response of each
original subsystem and the reduced one, the variation of absolute error between
each original subsystem and the reduced one and the poles distribution of the each
reduced subsystem (Chahlaoui and Dooren 2005 ; Diepold and Eid 2011 ).
The Fig. 17 presents the largest singular value of the frequency response of the
original switched linear system (order 1006) and reduced one (order 10) to a
frequency range by Iterative SVDDRK-SLS method.
Note that when a correlation over the entire frequency range shape with a low
error rate. The Fig. 18 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 inconsiderable over the entire frequency range.
The distribution poles in the complex plane of each subsystem is depicted in
Fig. 19 , all poles are negative real part, then the subsystems are stable.
The Fig. 20 presents the largest singular value of the frequency response of
the original switched linear system (order 348) and reduced one (order 24) to a
frequency range by Iterative SVDDRK-SLS method.
When a correlation over the entire frequency range shape with a low error rate.
The Fig. 21 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
inconsiderable over the entire frequency range.
The Fig. 22 presents the distribution poles in the complexes plane of each
subsystems, all poles are negative real part, then the subsystems are stable.

Fom Model Reduced System(sub−syste m1)

50

Exact1
IRK−SLS1

0

−50

10 −1 10 0 10 1 10 2 10 3 10 4

Frequency (Hz)

Fom Model Reduced System(sub−syste m1)

50

Exact2
IRK−SLS2

0

−50

10 −1 10 0 10 1 10 2 10 3 10 4

Frequency (Hz)

Fig. 17 Largest singular value of the frequency response of the original switched system of order
(1006) and reduced one of order (10) to a frequency range with iterative SVDDRK-SLS method