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 (Formula presented.) 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.