This paper addresses the exponential mean-square stability for a kind of switched Markovian jump systems, which have time-varying generally bounded transition rates and mode-dependent time delay. Since these transition rates are time-varying and generally bounded, they turn out to be more practical. In fact, those existing transition rates can be treated as special cases of the proposed ones in this paper. By constructing a new Lyapunov-Krasovskii function, sufficient conditions in a tractable form are derived for the exponential mean-square stability of the considered systems. For good measure, a numerical example is given to show the efficiency and potential of the proposed method.
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