## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 659251, 10 pages.

### Exponential ${L}_{2}\text{-}{L}_{\infty }$ Filtering for a Class of Stochastic System with Mixed Delays and Nonlinear Perturbations

#### Abstract

The delay-dependent exponential ${L}_{2}\text{-}{L}_{\infty }$ performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the ${L}_{2}\text{-}{L}_{\infty }$ filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs). By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed ${L}_{2}\text{-}{L}_{\infty }$ performance $\gamma$. Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 659251, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394806097

Digital Object Identifier
doi:10.1155/2013/659251

Mathematical Reviews number (MathSciNet)
MR3147895

Zentralblatt MATH identifier
06950807

#### Citation

Chen, Zhaohui; Huang, Qi. Exponential ${L}_{2}\text{-}{L}_{\infty }$ Filtering for a Class of Stochastic System with Mixed Delays and Nonlinear Perturbations. J. Appl. Math. 2013, Special Issue (2013), Article ID 659251, 10 pages. doi:10.1155/2013/659251. https://projecteuclid.org/euclid.jam/1394806097

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