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

• Published in: Abstract and Applied Analysis Vol. 2013; no. 2013; pp. 40 - 51-1105
• Main Authors: Luo, Yuqiang, Wei, Guoliang, Karimi, Hamid Reza, Wang, Licheng
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2013; Hindawi Puplishing Corporation; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Differential equations, Nonlinear; Filters (Mathematics); Mathematical research; Stochastic differential equations; Norway
• ISSN: 1085-3375; 1687-0409
• DOI: 10.1155/2013/814187

This paper deals with a robust H∞ 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∞ 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∞ 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.