Interval type-2 fuzzy filtering for singularly perturbed hidden Markov jump systems with general probabilities

This paper investigates the H∞ filtering problem for discrete-time nonlinear singularly perturbed Markov jump systems with hidden modes and general probabilities. An interval type-2 T-S fuzzy model is adopted to capture the nonlinearities and membership-function uncertainties, and a unified hidden Markov model-based framework is established to describe the mismatch between the true mode and the observed mode. Within this framework, both the transition probability matrix and the observation probability matrix are allowed to include known, uncertain, and unknown entries. An observation-mode-dependent interval type-2 fuzzy filter is developed, and sufficient membership-function-dependent LMI conditions are derived to ensure stochastic stability and a prescribed H∞ performance. The effectiveness of the proposed method is finally demonstrated by a tunnel-diode circuit example and a numerical example.