Interval Type-2 Fuzzy $\mathcal{H}_{\infty}$ Filtering for Singularly Perturbed Jumping Systems Based on Hidden Markov Model

This study investigates the fuzzy filtering problem for mode-constrained nonlinear Markov jump singularly perturbed systems and discusses its application in electronic circuits. The research initially employs an interval type-2 fuzzy modeling approach to address inherent system uncertainties and nonlinear characteristics. Building upon this foundation, an interval type-2 fuzzy filter correlated with observation mode yet independent of singularly perturbed parameters is constructed through integration of hidden Markov model and non-parallel distributed compensation technique. To simultaneously guarantee stochastic stability and achieve prescribed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}_{\infty}$</tex> performance specifications for the filtering error system, several membership-functiondependent sufficient conditions are derived. The introduction of relax matrices incorporating dual adjustable parameters for calculating the fuzzy filter gains. Ultimately, the effectiveness of developed methodology is validated by an electronic circuit model.