Chapter 2
Robust Filtering for Multi-model
Jumping System
During the last few decades, the state estimation or filter design problem has received
much attention due to the wide application in control and signal processing. For a
given system with unmeasurable states or a linear combination of states, the current
system states can be estimated by using the system’s past measurement information.
We can use the filtering scheme to obtain information of the current system states
through estimation. Since the well-known Kalman filter theory [246] was proposed
in the early 1960s, the study of state estimation and filtering has attracted great
attention by many researchers. In this chapter, the robust H ∞ filter and unbiased H ∞
filter problems are respectively designed for uncertain multi-model jumping system
with time-delays and uncertainties.
Different from the traditional Kalman filtering, H ∞ filtering method has attracted
much attention in the past few decades because it does not need to know the statistical
characteristics of unknown noise. The H ∞ filtering solution is to estimate the output
signal by constructing a suitable filter. Then, it aims to minimize the mapping of the
unknown disturbance signal to the output estimation error [247, 248] or not larger
than the specified H ∞ norm performance index condition [249, 250].
Firstly, we study the robust H ∞ filtering problem for multi-model jumping system with time-delays and uncertainties. By reconstructing the system, we obtain the
dynamics of the overall augmented error dynamic systems which involve unknown
inputs represented by disturbances, model uncertainties and time-delays. By choosing an appropriate Lyapunov–Krasovskii functional, we provide some sufficient conditions for the existence of the mode-dependent H ∞ filter for the reconstructed error
dynamic systems with time-delays and uncertainties.
Then, we study the unbiased H ∞ filtering problem for the multi-model jumping system with time-delays and uncertainties. Meanwhile, we also give a sufficient
condition to ensure the existence of the mode-dependent unbiased H ∞ filter for the
error dynamic systems with time-delays and uncertainties. Furthermore, we design
© 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_2
13
Robust Filtering for Multi-model
Jumping System
During the last few decades, the state estimation or filter design problem has received
much attention due to the wide application in control and signal processing. For a
given system with unmeasurable states or a linear combination of states, the current
system states can be estimated by using the system’s past measurement information.
We can use the filtering scheme to obtain information of the current system states
through estimation. Since the well-known Kalman filter theory [246] was proposed
in the early 1960s, the study of state estimation and filtering has attracted great
attention by many researchers. In this chapter, the robust H ∞ filter and unbiased H ∞
filter problems are respectively designed for uncertain multi-model jumping system
with time-delays and uncertainties.
Different from the traditional Kalman filtering, H ∞ filtering method has attracted
much attention in the past few decades because it does not need to know the statistical
characteristics of unknown noise. The H ∞ filtering solution is to estimate the output
signal by constructing a suitable filter. Then, it aims to minimize the mapping of the
unknown disturbance signal to the output estimation error [247, 248] or not larger
than the specified H ∞ norm performance index condition [249, 250].
Firstly, we study the robust H ∞ filtering problem for multi-model jumping system with time-delays and uncertainties. By reconstructing the system, we obtain the
dynamics of the overall augmented error dynamic systems which involve unknown
inputs represented by disturbances, model uncertainties and time-delays. By choosing an appropriate Lyapunov–Krasovskii functional, we provide some sufficient conditions for the existence of the mode-dependent H ∞ filter for the reconstructed error
dynamic systems with time-delays and uncertainties.
Then, we study the unbiased H ∞ filtering problem for the multi-model jumping system with time-delays and uncertainties. Meanwhile, we also give a sufficient
condition to ensure the existence of the mode-dependent unbiased H ∞ filter for the
error dynamic systems with time-delays and uncertainties. Furthermore, we design
© 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_2
13