Chapter 4
Finite-Frequency Robust Filtering for
Multi-model Jumping System
In this part, H ∞ filters are designed for multi-model jumping system with finite
frequency performance and multiple frequency restrictions, respectively.
Most filtering results related to multi-model jumping system are mainly based
on the entire frequency domain [251]; however, the filter design specifications are
often required in some finite frequency ranges. Therefore, ignoring finite frequency
intricacies in filter design may lead to conservative and poor filtering performance
results. To overcome these deficiencies, Iwasaki proposed the generalized Kalman–
Yakubovic–Popov (GKYP) lemma in 2005 [241], which offered a new perspective
on analysis and synthesis of the finite frequency filtering problem. Since then, many
scholars have examined finite frequency filtering and obtained corresponding results
[252]. However, most research findings on finite frequency filtering have only been
referring to single-mode systems. When refer to the finite frequency performance of
multi-model jumping system, the effect of mode jumping on the performance of the
whole system should be analyzed. This is the motivation of this chapter.
Firstly, we study the robust H ∞ filtering problems for multi-model jumping system with finite frequency band restriction. A derandomisation technique is explored
to transform the multi-model jumping system to an extended deterministic one, which
can infuse the effect of transition probabilities in finite frequency specifications analysis directly. For the obtained extended system, the finite frequency filter is designed
to satisfy the desired disturbance rejection level.
Then, considering the device requirement in practice, the multiple frequency filter
is designed for multi-model jumping system with low-frequency and high-frequency
bands noise. Combining with the definition of finite frequency, we develop the multiple frequency filtering scheme to reduce the engineering conservation of filtering
theory. The finite-frequency domain performance is satisfied by introducing the frequency information of external disturbances with specific band into the filter design.
Then in terms of LMIs techniques, sufficient conditions on the existence of robust
multiple frequency filter are presented and proved.
Finally, simulation results illustrate the validity of the proposed algorithm.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_4
51
Finite-Frequency Robust Filtering for
Multi-model Jumping System
In this part, H ∞ filters are designed for multi-model jumping system with finite
frequency performance and multiple frequency restrictions, respectively.
Most filtering results related to multi-model jumping system are mainly based
on the entire frequency domain [251]; however, the filter design specifications are
often required in some finite frequency ranges. Therefore, ignoring finite frequency
intricacies in filter design may lead to conservative and poor filtering performance
results. To overcome these deficiencies, Iwasaki proposed the generalized Kalman–
Yakubovic–Popov (GKYP) lemma in 2005 [241], which offered a new perspective
on analysis and synthesis of the finite frequency filtering problem. Since then, many
scholars have examined finite frequency filtering and obtained corresponding results
[252]. However, most research findings on finite frequency filtering have only been
referring to single-mode systems. When refer to the finite frequency performance of
multi-model jumping system, the effect of mode jumping on the performance of the
whole system should be analyzed. This is the motivation of this chapter.
Firstly, we study the robust H ∞ filtering problems for multi-model jumping system with finite frequency band restriction. A derandomisation technique is explored
to transform the multi-model jumping system to an extended deterministic one, which
can infuse the effect of transition probabilities in finite frequency specifications analysis directly. For the obtained extended system, the finite frequency filter is designed
to satisfy the desired disturbance rejection level.
Then, considering the device requirement in practice, the multiple frequency filter
is designed for multi-model jumping system with low-frequency and high-frequency
bands noise. Combining with the definition of finite frequency, we develop the multiple frequency filtering scheme to reduce the engineering conservation of filtering
theory. The finite-frequency domain performance is satisfied by introducing the frequency information of external disturbances with specific band into the filter design.
Then in terms of LMIs techniques, sufficient conditions on the existence of robust
multiple frequency filter are presented and proved.
Finally, simulation results illustrate the validity of the proposed algorithm.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. He and X. Luan, Multi-model Jumping Systems: Robust Filtering and Fault Detection,
https://doi.org/10.1007/978-981-33-6474-5_4
51