Mean-square bounded synchronization of fractional-order chaotic Lur’e systems under deception attack

This paper discussed the mean-square bounded synchronization (MSBS) of fractional-order chaotic Lur’e systems (FOCLSs) in the presence of deception attacks. Firstly, it was assumed that the channel of the controller to the actuator was subjected to stochastic deception attacks, which were modeled by the Bernoulli stochastic variable. Secondly, impulsive control was proposed to achieve the aim of the MSBS of FOCLSs. Moreover, the event-triggered mechanism (ETM) is added to the impulsive control to decrease the controller update times and save computing resources consumption. Applied the fractional-order calculus, the Laplace transform, and the definition of MSBS, sufficient criteria were derived to guarantee the MSBS of FOCLSs, with the criteria being dependent on the order of the system. The upper bound of the synchronization error is given for the error system under impulsive control and event-triggered impulsive control (ETIC), respectively. Finally, Chua’s circuit was employed to indicate the practicability of the MSBS of FOCLSs. •A low-consumption controller about fractional-order is adopted for the first time.•Deception attack is introduced into fractional-order chaotic Lur’e systems.•The event-triggered impulsive controller is used to save communication resources.