Event-Triggered $$H_{\infty }$$ Filtering for Discrete-Time Markov Jump Systems with Repeated Scalar Nonlinearities

Abstract

This paper is concerned with the $$H_{\infty }$$ filtering problem for discrete-time Markov jump systems with repeated scalar nonlinearities in an event-triggered communication scheme. An event-triggered scheme is proposed to determine whether the current data should be transmitted to the filter or not. Based on the time interval analysis approach, the discrete-time Markov jump system with network-induced delays under event-triggered communication scheme is converted into the discrete-time Markov jump time-delay system. By employing the positive-definite diagonally-dominant-type Lyapunov function technique, criteria are derived to guarantee the system is stochastically stable with a prescribed $$H_{\infty }$$ performance level. The correspondent filter and the event-triggered parameters are also solved. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.