H∞ Filtering for Multi-Rate Systems with State Saturation under Periodic Denial-of-Service and Deception Attacks

In this paper, $H_{\infty}$ filtering problem is investigated for multi-rate networked systems with state saturation suffering both random deception and periodic denial-of-service (DoS) attacks. The multi-rate phenomenon is considered, and the lifting technology is employed to transform the multi-rate system into a single rate one. State saturation is characterized by nonlinear inequality constraint. For the periodic cyber attacks, the model is set up which considers two situations consisting of the attack period and the sleeping period, besides, the occurrence of deception attacks is characterized by utilizing a random variable that follows the Bernoulli distribution. The purpose of this paper is to design a $H_{\infty}$ filter which takes into account state saturation as well as hybrid attacks. Sufficient condition for reaching both the asymptotic stability and the $H_{\infty}$ performance index of the system is obtained by using Lyapunov stability theory and stochastic analysis technique. The gain parameters of the filter are calculated through solving a linear matrix inequality. Eventually, a numerical example is provided to demonstrate the efficacy of the filter design approach.