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

This paper deals with a robust<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>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.