Novel adaptive filter design for complex‐valued network systems under hybrid cyber attacks

This paper is concerned with the problem of designing adaptive event‐triggered H∞$$ H\infty $$ filter for complex‐valued network system under complex‐valued hybrid cyber attack. Firstly, the main contribution of the article is to propose a complex‐valued adaptive event triggered strategy to improve the resource utilisation in the network channel. Secondly, during the modeling process of the filtering error model, we introduce complex‐valued stochastic deception attacks and replay attacks that follow the Bernoulli distribution, thereby forming the complex‐valued hybrid network attacks investigated in this paper. Sufficient conditions for the asymptotic stability of the designed complex‐valued filtered error system are derived using Lyapunov stability theory. In addition, the parameters of the filter are derived using the linear matrix inequality (LMI) method. Finally, a numerical simulation example is given to verify the feasibility of the proposed method. This paper addresses the design of an adaptive event‐triggered H∞$$ H\infty $$ filter for complex‐valued network systems under complex‐valued hybrid cyber attacks. We propose a complex‐valued adaptive event‐triggered strategy to enhance resource utilization in the network channel and introduce complex‐valued stochastic deception and replay attacks within the filtering error model, forming a complex‐valued hybrid network attack model. The paper establishes sufficient conditions for asymptotic stability using Lyapunov stability theory, and filter parameters are derived using the LMI method.