## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2012, Special Issue (2012), Article ID 710904, 11 pages.

### Finite-Time ${H}_{\infty }$ Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations

#### Abstract

This paper is concerned with the finite-time ${H}_{\infty }$ filtering problem for linear continuous time-varying systems with uncertain observations and 2-norm bounded noise. The design of finite-time ${H}_{\infty }$ filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state-space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite-time ${H}_{\infty }$ filtering problem is solved. A numerical example is given to illustrate the performance of the ${H}_{\infty }$ filter.

#### Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 710904, 11 pages.

Dates
First available in Project Euclid: 3 January 2013

https://projecteuclid.org/euclid.jam/1357178272

Digital Object Identifier
doi:10.1155/2012/710904

Mathematical Reviews number (MathSciNet)
MR2948146

Zentralblatt MATH identifier
1251.93049

#### Citation

Zhao, Huihong; Zhang, Chenghui. Finite-Time ${H}_{\infty }$ Filtering for Linear Continuous Time-Varying Systems with Uncertain Observations. J. Appl. Math. 2012, Special Issue (2012), Article ID 710904, 11 pages. doi:10.1155/2012/710904. https://projecteuclid.org/euclid.jam/1357178272

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