Finite-time secure synchronization for stochastic complex networks with delayed coupling under deception attacks: A two-step switching control scheme

This article is concerned with the finite-time secure synchronization (FNTS) in mean square for stochastic complex networks (SCNs) with time-varying delayed coupling under deception attacks, where attack is described by a Bernoulli's stochastic variable, and is performed in the communication channel between the controller and the actuator. With the help of an auxiliary function, a new Halanay inequality is developed for continuous differential stochastic functions. By utilizing the Lyapunov functional gradient inequality with variable coefficients, a criterion about the finite-time stability in mean square is established for nonlinear stochastic systems under the designed two-step attenuation scheme. In order to reduce controller update consumption and communication waste, a two-step switching control mechanism consisting of an event-triggered control (ETC) and a time-varying gain state feedback control, is devised to achieve the FNTS objective. By Lyapunov stability theory, inequality analysis technique and the proposed finite-time stability criterion, the finite-time synchronization conditions are addressed in terms of linear matrix inequality (LMIs), and the bound of stochastic settling time (SST) is estimated explicitly. Finally, a practical application example is given to illustrate the effectiveness of the proposed control scheme, and to verify the correctness of the analytical results.