This paper investigates an asynchronous H∞ control strategy for a class of discrete-time Markovian jump linear
system (MJLS) subject to hard time domain constraints. The word “asynchronous” means that the switching of candidate
controllers has a lag to the jump of system modes. First, new results on the mean square stability and H∞ performance
analysis for MJLS are given with average dwell time (ADT) bound by allowing the stochastic Lyapunov-like function
(LLF) to increase during the running time of each active mode. The internal relationship between ADT and transition
probabilities (TPs) is revealed by fully making use of the jump knowledge. Then, the asynchronous H∞ controller for
MJLS subject to input/output constraints is designed with the aid of a set of stochastic invariant ellipsoids. Moreover, the
domain of the admissible set is enlarged by constructing a set of polyhedral invariant sets on-line with the designed controller.
Finally, numerical examples are given to verify the potential of the developed results.