Adaptive Event‐Triggered Asynchronous Filtering for Piecewise Homogenous Markov Jump Systems via Singular Transformation

This article is devoted to develop an asynchronous event‐triggered filter for discrete‐time piecewise homogeneous Markov jump systems. By dual hidden Markov process, a type of more general model is constructed, such that more stochastic time‐variant systems can be described. Noting that communication resource is limited in some circumstances, a novel adaptive event‐triggered mechanism is employed that considering the effect of threshold alterations on system performance one seldom studied in the most existing works. Then, the interval type‐2 fuzzy theory is introduced to deal with the adaptive threshold with nonlinear features instead of the normal adaptive law. Combined with the proposed event‐triggered mechanism, a mode‐dependent event‐based filter is derived. Then, a novel design procedure with less conservatism is utilized to transform error dynamic into a singular one. By the help of the convex optimization techniques and Lyapunov methods, some sufficient conditions are presented to ensure the performance of the error system. Finally, an example is presented to demonstrate that this method is more effective than the existed strategies.