of the important methods to improve safety and reliability, which is to analyze and
deal with the characteristics of faults and then to detect and isolate them. How to
study and analyze the filtering and fault detection problems for multi-model
jumping systems has become a challenging work.
This book proposes the latest results of multi-model jumping systems divided
into nine chapters with three parts. The first part consists of Chap. 1, which provides
the background of multi-model jumping systems and gives some main definitions
and lemmas. The second part mainly includes Chap. 2 to Chap. 5, which studies the
filtering problems for multi-model jumping systems. The third part mainly includes
Chap. 6 to Chap. 9, which studies the fault detection problems for multi-model
jumping systems. The main contents of each chapter are given as:
Chapter 1 provides the background of multi-model jumping systems, robust
fitering and fault detection, finite-time and finite-frequency, including some main
definitions and lemmas. In Chap. 2, the problems of robust H ∞ filtering and
unbiased H ∞ filtering for multi-model jumping systems with time-delays and
uncertainties are considered. Then, Chap. 3 studies the problems of robust H ∞
filtering and L 2 -L ∞ filtering for multi-model jumping systems with time-delays and
uncertainties in finite-time interval. Chapter 4 firstly studies the robust H ∞ filtering
problem for multi-model jumping systems with finite frequency band restriction.
Then, the multiple frequency filter is designed for multi-model jumping systems
with low-frequency and high-frequency bands noise by considering the device
requirement in practice. In Chap. 5, the high-order moment H ∞ filtering problem
for multi-model jumping systems is addressed and a new approach is provided
based on GKYP lemma by considering the finite frequency characteristics with
unknown disturbances. Chapter 6 is concerned with the robust fault detection filter
and observer-based fault detection filter design problems for multi-model jumping
systems. Considering nonlinear multi-model jumping systems, the observer-based
robust fault detection problem is considered based on the T-S fuzzy method in
Chap. 7. Then, the filtering-based robust fault detection problem is considered of
fuzzy multi-model jumping systems in Chap. 8. Chapter 9 investigates the robust
fault detection design scheme for the LDI-based multi-model jumping systems.
In this book, Chap. 4 and Chap. 5 are written by Xiaoli Luan, and the other
chapters are written by Shuping He. The authors would like to thank Professor Fei
Liu, who has given a lot of help during the process of book writing. Professor Fei
Liu is also the supervisor of the authors as well as the contributor; he guides the
scientific research especially in the fields of finite-time control, finite frequency
control, robust filtering and fault detection of multi-model jumping systems. The
authors are also grateful to their family members for their great supports. In particular, the authors sincerely appreciate the collaborations and contributions of the
collaborators and students, such as Chengcheng Ren, Haiying Wan, Chang’an Han,
Peng Cheng, Jiancheng Wang and Xuefei Dong.
The work of this book is supported by the National Natural Science Foundation
of China under Grant 62073001, 61991402, the State Key Program of National
Natural Science Foundation of China under Grant 61833007, the Key Support
vi
Preface
deal with the characteristics of faults and then to detect and isolate them. How to
study and analyze the filtering and fault detection problems for multi-model
jumping systems has become a challenging work.
This book proposes the latest results of multi-model jumping systems divided
into nine chapters with three parts. The first part consists of Chap. 1, which provides
the background of multi-model jumping systems and gives some main definitions
and lemmas. The second part mainly includes Chap. 2 to Chap. 5, which studies the
filtering problems for multi-model jumping systems. The third part mainly includes
Chap. 6 to Chap. 9, which studies the fault detection problems for multi-model
jumping systems. The main contents of each chapter are given as:
Chapter 1 provides the background of multi-model jumping systems, robust
fitering and fault detection, finite-time and finite-frequency, including some main
definitions and lemmas. In Chap. 2, the problems of robust H ∞ filtering and
unbiased H ∞ filtering for multi-model jumping systems with time-delays and
uncertainties are considered. Then, Chap. 3 studies the problems of robust H ∞
filtering and L 2 -L ∞ filtering for multi-model jumping systems with time-delays and
uncertainties in finite-time interval. Chapter 4 firstly studies the robust H ∞ filtering
problem for multi-model jumping systems with finite frequency band restriction.
Then, the multiple frequency filter is designed for multi-model jumping systems
with low-frequency and high-frequency bands noise by considering the device
requirement in practice. In Chap. 5, the high-order moment H ∞ filtering problem
for multi-model jumping systems is addressed and a new approach is provided
based on GKYP lemma by considering the finite frequency characteristics with
unknown disturbances. Chapter 6 is concerned with the robust fault detection filter
and observer-based fault detection filter design problems for multi-model jumping
systems. Considering nonlinear multi-model jumping systems, the observer-based
robust fault detection problem is considered based on the T-S fuzzy method in
Chap. 7. Then, the filtering-based robust fault detection problem is considered of
fuzzy multi-model jumping systems in Chap. 8. Chapter 9 investigates the robust
fault detection design scheme for the LDI-based multi-model jumping systems.
In this book, Chap. 4 and Chap. 5 are written by Xiaoli Luan, and the other
chapters are written by Shuping He. The authors would like to thank Professor Fei
Liu, who has given a lot of help during the process of book writing. Professor Fei
Liu is also the supervisor of the authors as well as the contributor; he guides the
scientific research especially in the fields of finite-time control, finite frequency
control, robust filtering and fault detection of multi-model jumping systems. The
authors are also grateful to their family members for their great supports. In particular, the authors sincerely appreciate the collaborations and contributions of the
collaborators and students, such as Chengcheng Ren, Haiying Wan, Chang’an Han,
Peng Cheng, Jiancheng Wang and Xuefei Dong.
The work of this book is supported by the National Natural Science Foundation
of China under Grant 62073001, 61991402, the State Key Program of National
Natural Science Foundation of China under Grant 61833007, the Key Support
vi
Preface