Chapter 8
Filtering-Based Robust Fault Detection
of Fuzzy Multi-model Jumping System
With the development of modern industry, the requirements for product quality,
effectiveness, and safety are constantly increasing. FD scheme has received more
and more attention in the past two decades. The basic idea of FD is to build a
residual signal and a residual evaluation function, and apply the observer or filter to
detect the fault by an appropriate predefined threshold. When the residual evaluation
function value surpasses a predetermined threshold, a fault alarm is generated. This
chapter mainly investigates the robust H ∞ -norm-based FD method. This method
can be considered as a filtering-based robust FD method, which is suitable for robust
FD systems. To introduce performance indicators and express FD problems as an
optimization index, we can refer to [115] and the references therein. The filteringbased robust FD scheme introduces the H ∞ norm of the unknown input to the residual
signal and provides the H ∞ norm of the fault to the residual to evaluate the sensitivity
to faults. The filtering-based robust FD method is to make the error between the
residual and the fault (or weighted fault) as small as possible.
This chapter studies the design of robust FD filter (FDF) for nonlinear multimodel jumping system with uncertainties and time delays. Initially, we adopted
the T-S fuzzy model to approximate the nonlinear multi-model jumping system.
On this basis, the dynamic characteristics of the fuzzy robust FDF system and the
filter residual generator are proposed. Then, the FD problem is expressed as the
H ∞ filtering problem, so that the difference between the reference model (ideal
solution) and the robust FDF (real solution) to be designed tends to be small. Using
the constructed Lyapunov–Krasovsky functional method and LMIs [262], sufficient
conditions for the existence of fuzzy robust FDF are given and proved. Finally, the
problem of the robust FDF design is transformed into an optimization algorithm.
Simulation results determine the effectiveness of the proposed results.
© 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_8
139
Filtering-Based Robust Fault Detection
of Fuzzy Multi-model Jumping System
With the development of modern industry, the requirements for product quality,
effectiveness, and safety are constantly increasing. FD scheme has received more
and more attention in the past two decades. The basic idea of FD is to build a
residual signal and a residual evaluation function, and apply the observer or filter to
detect the fault by an appropriate predefined threshold. When the residual evaluation
function value surpasses a predetermined threshold, a fault alarm is generated. This
chapter mainly investigates the robust H ∞ -norm-based FD method. This method
can be considered as a filtering-based robust FD method, which is suitable for robust
FD systems. To introduce performance indicators and express FD problems as an
optimization index, we can refer to [115] and the references therein. The filteringbased robust FD scheme introduces the H ∞ norm of the unknown input to the residual
signal and provides the H ∞ norm of the fault to the residual to evaluate the sensitivity
to faults. The filtering-based robust FD method is to make the error between the
residual and the fault (or weighted fault) as small as possible.
This chapter studies the design of robust FD filter (FDF) for nonlinear multimodel jumping system with uncertainties and time delays. Initially, we adopted
the T-S fuzzy model to approximate the nonlinear multi-model jumping system.
On this basis, the dynamic characteristics of the fuzzy robust FDF system and the
filter residual generator are proposed. Then, the FD problem is expressed as the
H ∞ filtering problem, so that the difference between the reference model (ideal
solution) and the robust FDF (real solution) to be designed tends to be small. Using
the constructed Lyapunov–Krasovsky functional method and LMIs [262], sufficient
conditions for the existence of fuzzy robust FDF are given and proved. Finally, the
problem of the robust FDF design is transformed into an optimization algorithm.
Simulation results determine the effectiveness of the proposed results.
© 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_8
139