Annular Finite‐Time Stochastic H∞ Control for Singular Switching Markov Jump Systems Subject to Wiener Process: A Dual Asynchronous Control Strategy

ABSTRACT This paper investigates annular finite‐time stochastic control for singular switching Markov jump systems (SSMJSs) subject to the Wiener process by resorting to a dual asynchronous control scheme. In view of the impact of mode detection delay and incomplete information transmission, the double asynchronous controller consisting of switching signal asynchrony and stochastic jumping mode asynchrony is designed, which can more accurately characterize the mode mismatch between the operating subsystem and the controller. By combining the mode‐dependent stochastic double‐index Lyapunov function, the mode‐dependent average dwell‐time (MDADT) technique, and the hidden Markov model (HMM) approach, sufficient conditions are first proposed to ensure that the underlying systems carry out annular finite‐time admissibility (AFTA) with a prescribed performance level. Furthermore, appropriate auxiliary variable matrices are introduced to effectively decouple controller gains from Lyapunov matrices, and the asynchronous controllers are thereby successfully obtained by means of strict linear matrix inequalities (LMIs). Finally, a simulation example of the oil catalytic cracking process (OCCP) is given to verify the correctness of the obtained results.