LAUSR

In this brief, the problem of event-triggered mixed \begin{document}$ {H_\infty } $\end{document} and passive control for a class of discrete-time stochastic Markov jump systems with bounded inputs is addressed. In order to reduce the frequency of the variation of the controller, an effective triggered scheme, called event-triggered scheme, is proposed, where unlike the traditional triggered scheme, not all sampling states are required to be transmitted to the controller. The event-triggered controller, which is designed using Lyapunov functional analysis approach and slack matrices, can ensure that the resulting system is stochastically stable with a prescribed mixed \begin{document}$ {H_\infty } $\end{document} and passive performance index. Sufficient conditions in terms of linear matrix inequalities (LMIs) are derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.