4.3 Numeral Examples
71
while the blue solid line denotes the high-frequency performance. It is obvious from
Fig. 4.6 that both the expected low- and high-frequency specifications are guaranteed, which proves the effectiveness of the proposed approach. Moreover, the red
curve does not meet the constraint γ on the high frequency in Fig. 4.6. This displays
the merit of the proposed method that there is no need to satisfy the constraints in
full frequency bands to leave some margin for other performance of the considered
system.
4.4 Conclusions
For the multi-model jumping system with finite frequency performance restrictions,
we have studied the robust finite frequency and multiple frequency filtering problems.
With the help of the derandomization approach, the multi-model jumping system is
transformed to a deterministic one. Then the relationships between the transition rates
with finite frequency specifications are characterized in terms of LMIs, and sufficient
conditions on the existence of finite frequency filter and multiple frequency filter are
presented and proved. Two illustrative examples are employed to demonstrate the
effectiveness of the developed approaches.