Chapter 1
Introduction
In recent decades, the research on multi-model jumping systems has become more
and more extensive, and a lot of valuable results have been achieved. Multi-model
jumping system is a kind of special stochastic system. The research on this system
not only promotes the development of stochastic system theory, but also enriches the
research content of control theory. In fact, multi-model jumping system is also widely
used in practical industrial process. Many practical processes, such as manufacturing system, robot system, biological system, economic system, power system and
network communication system, can be modeled by multi-model jumping systems.
In the descriptions of this book, unless otherwise specified, we refer to multi-model
jumping system that follows Markov switching laws. This chapter mainly elaborates
the subject of the background and research status of multi-model jumping systems,
the main concepts and the theoretical basis of robust filtering and fault detection.
1.1 Background and Research Status of Multi-model
Jumping System
Multi-model jumping system that follows Markov switching laws was first proposed
by Krasovskii and lidskii [1] in the 1960s. It has been regarded as a special kind of
hybrid systems because it has two hybrid dynamic forms, that is, mode and state.
With the development of stochastic system theory and control theory, it has gradually
drawn the scholars’ attention and become a new research hotspot in the field of
control theory. It is found that the multi-model jumping system is actually a special
stochastic system, because the mode of the system is described by continuous-time
and discrete-state Markov process, and the state of the system is described by the
state space equation under each mode. Moreover, in each mode, the state space
equation is represented by a stochastic differential equation (or difference equation
© 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_1
1
Introduction
In recent decades, the research on multi-model jumping systems has become more
and more extensive, and a lot of valuable results have been achieved. Multi-model
jumping system is a kind of special stochastic system. The research on this system
not only promotes the development of stochastic system theory, but also enriches the
research content of control theory. In fact, multi-model jumping system is also widely
used in practical industrial process. Many practical processes, such as manufacturing system, robot system, biological system, economic system, power system and
network communication system, can be modeled by multi-model jumping systems.
In the descriptions of this book, unless otherwise specified, we refer to multi-model
jumping system that follows Markov switching laws. This chapter mainly elaborates
the subject of the background and research status of multi-model jumping systems,
the main concepts and the theoretical basis of robust filtering and fault detection.
1.1 Background and Research Status of Multi-model
Jumping System
Multi-model jumping system that follows Markov switching laws was first proposed
by Krasovskii and lidskii [1] in the 1960s. It has been regarded as a special kind of
hybrid systems because it has two hybrid dynamic forms, that is, mode and state.
With the development of stochastic system theory and control theory, it has gradually
drawn the scholars’ attention and become a new research hotspot in the field of
control theory. It is found that the multi-model jumping system is actually a special
stochastic system, because the mode of the system is described by continuous-time
and discrete-state Markov process, and the state of the system is described by the
state space equation under each mode. Moreover, in each mode, the state space
equation is represented by a stochastic differential equation (or difference equation
© 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_1
1