Chapter 3
Finite-Time Robust Filtering for
Multi-model Jumping System
In this chapter, the finite-time robust H ∞ filtering and L 2 − L ∞ filtering problems are
respectively designed for continuous multi-model jumping system with time-delays
and uncertainties. As is known to all, since the knowledge of Kalman filtering theory
[246] is introduced in 1960s, scholars have developed many filtering schemes, see, for
example, [198–202], and the references therein. Among these filtering approaches,
the H ∞ filtering [198] and L 2 − L ∞ filtering [199] have aroused our attention.
It is now worth pointing out that many scholars have paid attention to the convergence characteristic of dynamics within a finite-time interval [196]. As pointed in
Introduction, the concept of finite-time stability [142] and finite-time boundedness
[153] were proposed. Particularly, it is widely acknowledge that there exist inherent
parameter uncertainties [57] of many physical process. Based on the above consideration, the H ∞ filtering and L 2 − L ∞ filtering problems in finite-time interval for
multi-model jumping system are given in this chapter.
First, the robust finite-time H ∞ filtering problem for multi-model jumping system
with time-delays and uncertainties is studied. By establishing the state estimation filter, we construct an augmented dynamic error multi-model jumping system. According to LMIs techniques, the dynamic error system is finite-time bounded (FTB) with
a prescribed H ∞ performance index.
Then, the robust L 2 − L ∞ filtering problem for multi-model jumping system
with time-delays and uncertainties is also investigated. By designing a suitable
robust filter, we construct an error dynamic system. By selecting an appropriate
Lyapunov–Krasovskii functional and applying the L 2 − L ∞ filtering approach, the
error dynamic multi-model jumping system is FTB with a given L 2 − L ∞ index.
Finally, two simulation examples are exploited to illustrate the feasibility of our
proposed methods.
© 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_3
29
Finite-Time Robust Filtering for
Multi-model Jumping System
In this chapter, the finite-time robust H ∞ filtering and L 2 − L ∞ filtering problems are
respectively designed for continuous multi-model jumping system with time-delays
and uncertainties. As is known to all, since the knowledge of Kalman filtering theory
[246] is introduced in 1960s, scholars have developed many filtering schemes, see, for
example, [198–202], and the references therein. Among these filtering approaches,
the H ∞ filtering [198] and L 2 − L ∞ filtering [199] have aroused our attention.
It is now worth pointing out that many scholars have paid attention to the convergence characteristic of dynamics within a finite-time interval [196]. As pointed in
Introduction, the concept of finite-time stability [142] and finite-time boundedness
[153] were proposed. Particularly, it is widely acknowledge that there exist inherent
parameter uncertainties [57] of many physical process. Based on the above consideration, the H ∞ filtering and L 2 − L ∞ filtering problems in finite-time interval for
multi-model jumping system are given in this chapter.
First, the robust finite-time H ∞ filtering problem for multi-model jumping system
with time-delays and uncertainties is studied. By establishing the state estimation filter, we construct an augmented dynamic error multi-model jumping system. According to LMIs techniques, the dynamic error system is finite-time bounded (FTB) with
a prescribed H ∞ performance index.
Then, the robust L 2 − L ∞ filtering problem for multi-model jumping system
with time-delays and uncertainties is also investigated. By designing a suitable
robust filter, we construct an error dynamic system. By selecting an appropriate
Lyapunov–Krasovskii functional and applying the L 2 − L ∞ filtering approach, the
error dynamic multi-model jumping system is FTB with a given L 2 − L ∞ index.
Finally, two simulation examples are exploited to illustrate the feasibility of our
proposed methods.
© 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_3
29