## Journal of Applied Mathematics

### Robust ${H}_{\infty }$ Filtering for Uncertain Discrete-Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time-Varying Delay

#### Abstract

The robust filtering problem for a class of uncertain discrete-time fuzzy stochastic systems with sensor nonlinearities and time-varying delay is investigated. The parameter uncertainties are assumed to be time varying norm bounded in both the state and measurement equations. By using the Lyapunov stability theory and some new relaxed techniques, sufficient conditions are proposed to guarantee the robustly stochastic stability with a prescribed ${H}_{\infty }$ performance level of the filtering error system for all admissible uncertainties, sensor nonlinearities, and time-varying delays. These conditions are dependent on the lower and upper bounds of the time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 402480, 25 pages.

Dates
First available in Project Euclid: 5 April 2013

https://projecteuclid.org/euclid.jam/1365174344

Digital Object Identifier
doi:10.1155/2012/402480

Mathematical Reviews number (MathSciNet)
MR3005218

Zentralblatt MATH identifier
1263.93132

#### Citation

Hua, Mingang; Cheng, Pei; Fei, Juntao; Zhang, Jianyong; Chen, Junfeng. Robust ${H}_{\infty }$ Filtering for Uncertain Discrete-Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time-Varying Delay. J. Appl. Math. 2012 (2012), Article ID 402480, 25 pages. doi:10.1155/2012/402480. https://projecteuclid.org/euclid.jam/1365174344