Adaptive intermittent control for exponential synchronization of directed networks with complex-variable systems and distributed delays coupling

In this paper, adaptive exponential synchronization of directed networks with complex-variable systems and distributed delays coupling is investigated. An adaptive nonperiodical intermittent control scheme is adopted to realize exponential synchronization of such complex-variable directed dynamical networks. Based on the complex inequality, piecewise analysis method and Lyapunov stability theory, some sufficient conditions guaranteeing globally exponential synchronization are established. Different from previous works, here the designed adaptive update law for intermittent feedback control gain does not explicitly depend on time, which makes the adaptive nonperiodical intermittent control technique more convenient to implement in realistic applications. Moreover, it is indicated that the established synchronization criteria depend on the control rates rather than the control periods or control widths, and therefore the control periods can be optionally chosen for practical problems. Finally, numerical simulations are given to illustrate the effectiveness of the derived theoretical results.