$H_{\infty}$ Filtering for Cyber-Physical Systems with Random Multi-Step Transmission Delays via Delta Operator

The
$H_{\infty}$
filtering problem for Cyber-physical systems (CPSs) with random multi-step transmission delays is investigated. The delta operator approach is used to solve the problem of numerical instability. A mathematical expression with stochastic processes is built to express random multi-step transmission delays. Sufficient conditions of stochastic stability for the filtering error system with
$H_{\infty}$
performance are given by linear matrix inequalities (LMIs) and Lyapunov-Krasovskii functional in delta domain. The explicit expression of the desired
$H_{\infty}$
filter is also obtained. At last, a target tracking system as the example is shown to indicate the effectiveness of the proposed approach.