Fuzzy-model-based ℋ∞ filtering for discrete-time singular Markov jump nonlinear systems against hybrid attacks

Abstract

This paper investigates the H ∞ filtering problem for a class of discrete-time singular Markov jump nonlinear systems against hybrid attacks via a fuzzy-model-based method, in which the hybrid attacks contain deception attacks and denial of service attacks. Two random variables subject to the Bernoulli distribution are used to describe whether the hybrid attacks are encountered during the measurement output of the original system being transmitted to the filter. By using linear matrix inequality technology and Lyapunov stability theory, some sufficient conditions are given to guarantee the considered systems are stochastically admissible and meet H ∞ performance index γ. The design approach of the secure filter and a specific form to acquire the expected secure filter gains are obtained, respectively. Finally, to demonstrate the effectiveness of the proposed approach, both a numerical example and a practical example are provided.