Finite-Time $H_{\infty}$ Filtering for Markov Jump Systems Under Deception Attacks and Delays

In this article, the problem of finite-time $H_{\infty}$ filtering design is studied for Markov jump systems (MJSs) with deception attacks and delays. Considering that data transmission networks between the system and filter will be subject to deception attacks and delays, a switching filter is designed by current states and modes as well as delayed states and modes. Since there are non-Markov jumps caused by the current mode and the delayed mode in the error dynamic systems, an extended state space method is employed to reconstruct it as switched error dynamic MJSs. By selecting multiple Lyapunov functionals, nonlinear sufficient conditions are given to ensure the finite-time boundedness and $H_{\infty}$ performance of the switched error dynamic MJSs. In order to deal with the derived nonlinear conditions without introducing conservatism, a combination of genetic algorithms and linear matrix inequality tools is used to solve filter gains. Simultaneously, a multiobjective optimization between the finite-time boundary of system states and $H_{\infty}$ performance index can be realized by the obtained filter gains. Simulation results are provided to illustrate the feasibility and effectiveness of the proposed approach.