$\mathcal{H}_∞$ filtering for switched nonlinear systems: A state projection method

Lin Du; Yun Zhang

doi:10.3934/jimo.2017035

Article Contents

2018, Volume 14, Issue 1: 19-33. Doi: 10.3934/jimo.2017035

This issue Previous Article The optimal cash holding models for stochastic cash management of continuous time Next Article A note on a Lévy insurance risk model under periodic dividend decisions

$\mathcal{H}_∞$ filtering for switched nonlinear systems: A state projection method

Lin Du^1, , and
Yun Zhang^2,

1.
School of Environment and Resource, Southwest University of Science and Technology, Mianyang 621000, China
2.
Mianyang Polytechnic, Mianyang 621000, China

* Corresponding author: Lin Du
* Corresponding author: Lin Du

Received: March 31, 2015

Revised: January 31, 2017

Early access: March 2017

Published: January 2018

This work was supported by the National Natural Science Foundation of China under Grant No. 61603312.

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Abstract

In this paper, the $\mathcal{H}_∞$ filtering problem of switched nonlinear system with linear hyper plane switching surface is investigated. A state projection method is introduced to ensure the stability of error system and guarantee a prescribed disturbance attenuation level in the $\mathcal{H}_∞$ sense, by designing filter gains for each subsystem via solving a set of LMIs and formulating a state projection relation for filter state at switching instant. It is worthwhile to note that the state projection relation is deduced by both Lyapunov functions and the switching surface, which implies the state projection method is suitable for switched system with linear hyper plane switching surface. Finally, a numerical example is provided to illustrate our theoretic findings in this paper.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Illustration of state projection approach

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Figure 2. Illustration of projection of filter state

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Figure 3. State response of $x_1 (-)$ and $x_2 (\cdots)$

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Figure 4. State response of $\hat x_1 (-)$ and $\hat x_2 (\cdots)$

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Figure 5. Response of $z (-)$ and $\hat z (\cdots)$

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Figure 6. Response of $\tilde z = z-\hat z$

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