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Abstract-This paper studies the problem of passivity-based asynchronous control for discrete-time Markov jump systems.The asynchronization phenomenon appears between the system modes and controller modes, which is described by a hidden Markov model. Accordingly, the resultant closed-loop system is named as a hidden Markov jump system. By utilizing the matrix inequality technique, three equivalent sufficient conditions are proposed to ensure the stochastic passivity of the hidden Markov jump systems. Based on the established conditions, the design of asynchronous controller, which covers synchronous controller and mode-independent controller as special cases, is addressed. A numerical example is given to demonstrate the effectiveness of the derived results.

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