LAUSR

This article investigates the hidden Markov model based H∞ filter design problem for the singular semi‐Markov jump systems (SSMJSs). The considered semi‐Markov process is a generalization of Markov process, which can eliminate the restriction on the exponential distribution of sojourn time. Besides, the hidden Markov model based filter is introduced to tackle the asynchronous phenomenons occurred between the system modes and filter modes. To ensure the stochastic stability of the SSMJSs and derive solvable filter parameters, a filter design technic is constructed. First, the direct evolution of the states between two arbitrary close time instants is constructed from the filtering error system according to slow‐fast decomposition, sufficient conditions are then proposed based on the consistent projector of the filtering error system and the constructed direct state evolution. Second, a new linear decoupling strategy is presented to deal with the coupled terms under the established stability conditions, which further derives the desired hidden Markov model based H∞ filter parameters. A numerical example is given to illustrate the effectiveness of the proposed method.