Hybrid Event-Triggered Filtering for Nonlinear Markov Jump Systems With Stochastic Cyber-Attacks

This paper studies the problem of $H_{\infty }$ filtering for nonlinear Markov jump systems based on Takagi-Sugeno model. Firstly, we propose a hybrid event-triggered mechanism with an adjustable threshold, which not only helps to save more limited communication resources, but also excludes Zeno behavior while preserving the merits of continuous triggering. Secondly, given the threat of cyber-attacks to network security, a stochastic variable is introduced to describe the considered deception attacks in filter design. Thirdly, a less restrictive Lyapunov-Krasovskii functional (LKF), which is not required to be continuous and positive definite in a triggering interval, is constructed to establish sufficient condition on the exponential mean-square stability for the filtering error system with a weighted $H_{\infty }$ performance. Meanwhile, co-design of the desired filter and event-triggered mechanism is achieved. Finally, a tunnel diode circuit system is provided to illustrate the effectiveness and advantage of the obtained results.