Finite-Time Asynchronous H∞ Nonfragile Control for Markov Jump Systems with Time-Varying Mode Detection Probabilities

This work discusses the finite-time asynchronous H-infinity control problem for Markov jump systems in the presence of phenomena that the mode information is hidden and there may exist inaccuracies in controller gains. The hidden mode information is estimated by an hidden Markov model with time-varying mode detection probabilities. Based on the finite-time stability theory and the hidden Markov model based approach, two criteria are provided for analyzing the finitetime H-infinity performance of the considered system and the corresponding finite-time asynchronous H-infinity controller design method is developed. Finally, the theoretical results are verified by a numerical example.