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

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.