## Abstract and Applied Analysis

### Deconvolution Filtering for Nonlinear Stochastic Systems with Randomly Occurring Sensor Delays via Probability-Dependent Method

#### Abstract

This paper deals with a robust ${H}_{\mathrm{\infty }}$ deconvolution filtering problem for discrete-time nonlinear stochastic systems with randomly occurring sensor delays. The delayed measurements are assumed to occur in a random way characterized by a random variable sequence following the Bernoulli distribution with time-varying probability. The purpose is to design an ${H}_{\mathrm{\infty }}$ deconvolution filter such that, for all the admissible randomly occurring sensor delays, nonlinear disturbances, and external noises, the input signal distorted by the transmission channel could be recovered to a specified extent. By utilizing the constructed Lyapunov functional relying on the time-varying probability parameters, the desired sufficient criteria are derived. The proposed ${H}_{\mathrm{\infty }}$ deconvolution filter parameters include not only the fixed gains obtained by solving a convex optimization problem but also the online measurable time-varying probability. When the time-varying sensor delays occur randomly with a time-varying probability sequence, the proposed gain-scheduled filtering algorithm is very effective. The obtained design algorithm is finally verified in the light of simulation examples.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 814187, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393447716

Digital Object Identifier
doi:10.1155/2013/814187

Mathematical Reviews number (MathSciNet)
MR3068873

Zentralblatt MATH identifier
07095385

#### Citation

Luo, Yuqiang; Wei, Guoliang; Karimi, Hamid Reza; Wang, Licheng. Deconvolution Filtering for Nonlinear Stochastic Systems with Randomly Occurring Sensor Delays via Probability-Dependent Method. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 814187, 12 pages. doi:10.1155/2013/814187. https://projecteuclid.org/euclid.aaa/1393447716

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