HMM-Based Asynchronous <i>H</i> _∞ Filtering for Fuzzy Singular Markovian Switching Systems With Retarded Time-Varying Delays

Abstract

This article reports our study on asynchronous H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for fuzzy singular Markovian switching systems with retarded time-varying delays via the Takagi-Sugeno fuzzy control technique. The devised parallel distributed compensation fuzzy filter modes are described by a hidden Markovian model, which runs asynchronously with that of the original fuzzy singular Markovian switching delayed system. The fuzzy asynchronous filtering dealt with in this article contains synchronous and mode-independent filtering as special cases. Novel admissibility and filtering conditions are derived in terms of linear matrix inequalities so as to ensure the stochastic admissibility and the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance level. Simulation examples including a singlelink robot arm are employed to demonstrate the correctness and effectiveness of the proposed fuzzy asynchronous filtering technique.