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

Abstract

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.