Fuzzy-Model-Based $H_{\infty }$ Control for Markov Jump Nonlinear Slow Sampling Singularly Perturbed Systems With Partial Information

This paper concentrates on the fuzzy-model-based <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> control for Markov jump nonlinear slow sampling singularly perturbed systems with partial information. The partial information problems including partial information on the transition probabilities of the Markov chain, on the Markov state, and on detection probabilities are taken into account simultaneously. A new hidden Markov model (HMM), in which some elements need not be known, is introduced to formulate the partial information problems. Some criteria on <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance analysis and the existence of the desired HMM-based asynchronous fuzzy controller are derived. An optimized relaxation matrix is introduced to improve the decoupling method such that the obtained HMM-based asynchronous fuzzy controller is less conservative. Finally, two examples show the availability of the HMM-based asynchronous controller design procedures.