Finite-time synchronization of fully complex-valued networks with or without time-varying delays via intermittent control

This paper explores finite-time (F-T) synchronization for a type of fully complex-valued (C-V) networks with or without delays by proposing intermittent control schemes but without using the ordinary separation technique. Above all, the vector signum function in complex field is proposed as the generalization of real-valued counterpart, which is critical to the control design in complex field and the construction of Lyapunov functions. To realize F-T synchronization, several complex-valued intermittent controllers, only dependent of the information of controlled nodes, are designed on the addressed complex-valued networks, which are different from the design on the divided real-valued subsystems. In the theoretical analysis, some nontrivial Lyapunov functionals and functions are constructed by virtue of the proposed signum function and some inequalities are developed in complex domain to establish criteria of F-T synchronization. Finally, some numerical examples are performed to reveal the effectiveness of the derived results and the practicality of the proposed control strategies.