HMM-Based Fuzzy Control for Nonlinear Markov Jump Singularly Perturbed Systems With General Transition and Mode Detection Information

In this article, the hidden Markov model (HMM)-based fuzzy control problem is addressed for slow sampling model nonlinear Markov jump singularly perturbed systems (SPSs), in which the general transition and mode detection information issue is considered. The general information issue is formulated as the one with not only the transition probabilities (TPs) and the mode detection probabilities (MDPs) being partly known but also with the certain estimation errors existing in the known elements of them. This formulation covers the cases with both the TPs and the MDPs being fully known, or one of them being fully known but another being partly known, or both them being partly known but without the certain estimation errors, which were considered in some previous literature. By utilizing the HMM with general information, some strictly stochastic dissipativity analysis criteria are derived for the slow sampling model nonlinear Markov jump SPSs. In addition, a unified HMM-based fuzzy controller design methodology is established for slow sampling model nonlinear Markov jump SPSs such that a fuzzy controller can be designed depending on whether the fast dynamics of the systems are available or not. A numerical example and a tunnel diode circuit are finally used to illustrate the validity of the obtained results.