H∞ filtering for non-linear systems with stochastic sensor saturations and Markov time delays: The asymptotic stability in probability

This study is concerned with the filtering problem for a class of non-linear systems with stochastic sensor saturations and Markovian measurement transmission delays, where the asymptotic stability in probability is considered. The sensors are subject to random saturations characterised by a Bernoulli distributed sequence. The transmission time delays are governed by a discrete-time Markov chain with finite states. In the presence of the non-linearities, stochastic sensor saturations and Markovian time delays, sufficient conditions are established to guarantee that the filtering process is asymptotically stable in probability without disturbances and also satisfies the H∞ criterion with respect to non-zero exogenous disturbances under the zero-initial condition. Moreover, it is illustrated that the results can be specialised to linear filters. Two simulation examples are presented to show the effectiveness of the proposed algorithms.This work was supported by National Natural Science Foundation of China under Grants 61490701, 61290324, 61273156, 61473163, and 61210012, and Research Fund for the Taishan Scholar Project of Shandong Province of China, and Jiangsu Provincial Key Laboratory of E-business at Nanjing University of Finance and Economics of China under Grant JSEB201301, and Tsinghua University Initiative Scientific Research Program