4
1 Introduction
noise or external disturbances with known spectral density. Since the Kalman filtering
method and Luenberger’s observer theory were proposed, many scholars have done
a lot of pioneering work on state estimation which can be widely used in aerospace,
navigation and industrial process control.
However, it should be pointed out that in many industrial applications, many
dynamical systems contain uncertain parameters and the accurate system models
are difficult to obtain. In this case, we can refer to robust filtering schemes. This
method considers the uncertainties in the system and designs a filter to make the
filtering error dynamic systems be asymptotically stable and meet the given filtering
performance index. The main robust filtering methods include H ∞ estimation and
L 2 − L ∞ estimation. H ∞ estimation first assumes that the external disturbance signal
of the system is energy-bounded. The main design idea is to make the H ∞ norm of the
transfer function of the filtering error dynamic system, i.e., the transfer function from
the external disturbance signal to the filtering error signal, be less than the given value.
L 2 − L ∞ estimation also assumes that the external disturbance signal of the system
is energy-bounded. Different from H ∞ estimation, the main design ideas is to make
the filtering error dynamic system have certain L 2 − L ∞ disturbance attenuation
performance; it is also known as energy-to-peak filtering. In addition, there are many
other robust filtering methods, such as robust L 1 estimation (peak-to-peak filtering),
robust dissipative estimation, robust guaranteed performance filtering, robust passive
filtering, etc.
For linear multi-model jumping system, de Souza et al. respectively studied the
H ∞ filtering [81] and robust H ∞ filtering [82] in 1996. Wang et al. discussed the
filtering problem of non-linear multi-model jumping system in [83]; then Wang et
al. designed a full order filter, and studied the robust filtering problem of a class
of discrete-time linear multi-model jumping system by means of Ricatti equation
[84]. In 2006, Shi et al. proposed a robust filter design scheme for a class of delaydependent continuous-time multi-model jumping system [85]. For other conclusions
on the filtering of multi-model jumping system, we can refer to [86–108].
On the other hand, with the development of society, science and technology, modern engineering systems are becoming larger and more complicated, and the demands
for plant safety and reliability are important. In such large-scale and complex systems,
once an accident occurs, it may lead to casualties and huge property losses. In 1986,
the Chernobyl nuclear power plant in former Soviet Union had a nuclear leakage
accident, which caused very serious consequences. More than 400,000 people were
killed and injured, and the bad influence is still lingering. In 2011, the Fukushima
nuclear power plant in Japan suffered a nuclear leak due to the earthquake, which
caused a worse impact than the Chernobyl nuclear accident. The aftermath of the
1986 U.S. space shuttle Challenger was not over, and the space shuttle Columbia
disintegrated over Texas in 2003.
All these disasters show the importance of system safety and reliability in the
development of high technology, and one of the important methods to improve these
safety and reliability is fault detection and diagnosis. This also makes fault detection
technology be a hot topic in the research field and have been widely concerned. Fault
detection and diagnosis technology generally refers to the fault diagnosis technol-
1 Introduction
noise or external disturbances with known spectral density. Since the Kalman filtering
method and Luenberger’s observer theory were proposed, many scholars have done
a lot of pioneering work on state estimation which can be widely used in aerospace,
navigation and industrial process control.
However, it should be pointed out that in many industrial applications, many
dynamical systems contain uncertain parameters and the accurate system models
are difficult to obtain. In this case, we can refer to robust filtering schemes. This
method considers the uncertainties in the system and designs a filter to make the
filtering error dynamic systems be asymptotically stable and meet the given filtering
performance index. The main robust filtering methods include H ∞ estimation and
L 2 − L ∞ estimation. H ∞ estimation first assumes that the external disturbance signal
of the system is energy-bounded. The main design idea is to make the H ∞ norm of the
transfer function of the filtering error dynamic system, i.e., the transfer function from
the external disturbance signal to the filtering error signal, be less than the given value.
L 2 − L ∞ estimation also assumes that the external disturbance signal of the system
is energy-bounded. Different from H ∞ estimation, the main design ideas is to make
the filtering error dynamic system have certain L 2 − L ∞ disturbance attenuation
performance; it is also known as energy-to-peak filtering. In addition, there are many
other robust filtering methods, such as robust L 1 estimation (peak-to-peak filtering),
robust dissipative estimation, robust guaranteed performance filtering, robust passive
filtering, etc.
For linear multi-model jumping system, de Souza et al. respectively studied the
H ∞ filtering [81] and robust H ∞ filtering [82] in 1996. Wang et al. discussed the
filtering problem of non-linear multi-model jumping system in [83]; then Wang et
al. designed a full order filter, and studied the robust filtering problem of a class
of discrete-time linear multi-model jumping system by means of Ricatti equation
[84]. In 2006, Shi et al. proposed a robust filter design scheme for a class of delaydependent continuous-time multi-model jumping system [85]. For other conclusions
on the filtering of multi-model jumping system, we can refer to [86–108].
On the other hand, with the development of society, science and technology, modern engineering systems are becoming larger and more complicated, and the demands
for plant safety and reliability are important. In such large-scale and complex systems,
once an accident occurs, it may lead to casualties and huge property losses. In 1986,
the Chernobyl nuclear power plant in former Soviet Union had a nuclear leakage
accident, which caused very serious consequences. More than 400,000 people were
killed and injured, and the bad influence is still lingering. In 2011, the Fukushima
nuclear power plant in Japan suffered a nuclear leak due to the earthquake, which
caused a worse impact than the Chernobyl nuclear accident. The aftermath of the
1986 U.S. space shuttle Challenger was not over, and the space shuttle Columbia
disintegrated over Texas in 2003.
All these disasters show the importance of system safety and reliability in the
development of high technology, and one of the important methods to improve these
safety and reliability is fault detection and diagnosis. This also makes fault detection
technology be a hot topic in the research field and have been widely concerned. Fault
detection and diagnosis technology generally refers to the fault diagnosis technol-