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This paper deals with a state-feedback control scheme for nonlinear stochastic systems with Markovian switching. First, we present the results on the practically $ {p}$ -moment exponential stability with respect to an additional disturbance and the practically $ {p}$ -moment asymptotic stability relying on a specific event. However, elements in this event are hard to be observed directly. The main aim of this paper is to develop a self-triggered sampling rule to overcome this difficulty. By applying the improved monotone growth condition, Itô’s formula, Fubini’s theorem, Gronwall inequality, and comparison lemma, we establish a novel lemma to estimate the lower bound and upper bound of second-moment for state and error, respectively. Moreover, we also establish the practically asymptotic stability in mean square with the help of Jensen’s inequality technique, properties of $ {\mathcal {K}}$ -function and result on $ {p}$ -moment input-to-state stability. Furthermore, from Lipschitz continuity and monotonicity of functions, we obtain the value of the maximum triggering interval based on lasted-observed state. Finally, we give some remarks and discussions to show the significance of our results by comparing with those in the previous literature. [ABSTRACT FROM AUTHOR]

This paper investigates a class of discrete-time stochastic nonlinear systems with external disturbances. To obtain the stability of the suggested system, we develop an event-triggered mechanism which is more general than those given in previous literatures. On this basis, many techniques such as stochastic analysis theory, classified discussion, comparison principle and reduction to absurdity are successfully applied in this paper. Under some suitable conditions, the asymptotic stability in mean square in the case of the state-dependent external disturbance and the input-to-state stability in mean square in the case of the state-independent external disturbance are obtained. Finally, some discussions and remarks are provided to show the significance of our results. • The event-triggered state-feedback control of discrete-time stochastic nonlinear systems is studied. • The input-to-state stability takes into account the influence of the initial state for the future state of the system. • Our work considers discrete-time stochastic nonlinear systems with external disturbances, which is rare and challenging. • The asymptotic stability and input-to-state stability in mean square under the state-independent external disturbance are obtained. [ABSTRACT FROM AUTHOR]