Reliable filtering of nonlinear Markovian jump systems: the continuous-time case

Abstract

This paper is concerned with the reliable ℒ ₂ - ℒ ∞ filter design problem for the nonlinear continuous-time Markov jump systems based on Takagi-Sugeno fuzzy model. A stochastic variable is introduced to describe the encountered sensor failures, the value of which is dependent on the considered plant mode based on a hidden Markov process. In practice, generally the information on plant modes is not fully accessible to the reliable filter, which results in the nonsynchronous phenomena between the modes of involved plant and filter, and has a negative effect on the system performance. A hidden Markov model is also adopted to depict such kinds of nonsynchronous phenomena. The filtering error systems are called fuzzy dual hidden Markov jump systems. A sufficient condition, associated to the modes of the plant, sensor failures, and the filter are proposed for the filtering error systems to ensure the stochastic stability and guaranteed ℒ ₂ - ℒ ∞ performance, based on which the existence condition and explicit design method of a nonsynchronous filter are both given. Finally, two simulation examples illustrate the effectiveness of the proposed approach.