Non-fragile <i>H</i><SUB align="right">∞ control for 2D Markov jump systems with partially unknown probabilities and its application in metal rolling process

This article studies the asynchronous H∞ non-fragile control problem of two-dimensional Markov jump systems with imperfect probability information based on the Roesser systems. First, to make the system better simulate actual engineering applications, its transition probability and observation probability are considered to be completely known, partially unknown and completely unknown. Second, the hidden Markov model addresses the asynchronous phenomenon between the controller and the system, given that the system mode might not be precisely achieved in the actual environment. Simultaneously, non-fragile control is used to overcome the influence of controller gain fluctuation during the action process. Furthermore, a suitable Lyapunov function is constructed, and the associated theorem is used to deduce adequate requirements for the closed-loop system's stability. Lastly, the industrial steel rolling process and the Darboux equation example are used to confirm the feasibility of the suggested asynchronous non-fragile controller.