Further results on synchronization of chaotic Lur'e systems based on aperiodic time-triggered intermittent control

Aperiodic time-triggered intermittent control (ATIC) is presented to investigate the exponential synchronization issue of chaotic Lur'e systems (CLSs). In our work, for CLSs, the mathematical expression of ATIC is put forward initially. Different from time-triggered intermittent control (TIC), ATIC allows aperiodic sampling. The aperiodic sampling characteristic of ATIC makes it more flexible and adaptable in complex environments, which greatly increases its applications. Then, for the deduced ATIC error system, a key lemma is established, which demonstrates that, on control or free time intervals, the bound of the error vector norm at any instance can be described by the multiple of its norm at initial instance. Further, based on the lemma and a mixed time-dependent Lyapunov functional (MTLF), the exponential stability theorem is given for the deduced ATIC error system. Consequently, the exponential synchronization criterion with less conservativeness is obtained for CLSs via ATIC. With its aid, the design method of ATIC is proposed. Finally, the validity and superiority of ATIC are verified by a simulation example.