H∞ and l2−l∞ finite-horizon filtering with randomly occurring gain variations and quantization effects

This paper investigates the H∞ and l2−l∞ filtering problem for discrete stochastic nonlinear system with randomly occurring gain variations and quantization effects over a finite horizon. The system under consideration is subject to time-varying parameters and exogenous signals. A Bernoulli distributed white sequence with a known conditional probability is introduced to describe the binary switching phenomenon between two types of nonlinear disturbances. The randomly occurring filter gain variations are utilized to express the random change of filter parameters that is governed by a binary sequences taking values on 0 or 1. Moreover, the quantization effects of measurements are also taken into account where a form of logarithmic quantizer is applied. By using the recursive linear matrix inequalities (RLMIs) approach, sufficient conditions are established for the existence of the desired finite-horizon filter to guarantee the H∞ and l2−l∞ performance specifications at the same time. A numerical example is proposed to show the correctness and effectiveness of the proposed design method.