Time-delay and unavailability of system states bring extra difficulties to synchronization of chaotic systems. This paper investigates observer-based synchronization of time-delay complex-variable chaotic systems (CVCSs) with complex parameters. Differing from the existing works that considered time delay only in the linear term of some special CVCSs, the two cases of time delay in and out of nonlinear terms in general CVCSs are considered here, respectively. In addition, for the case that system states are not available for control, an observer-based output feedback control approach is developed to estimate the system states and guarantee the time-delay CVCSs to achieve synchronization. Moreover, by combining Lyapunov–Krasovskii function with linear matrix inequality in the complex field, two sufficient criteria are derived to ensure complete synchronization of time-delay CVCSs. Finally, a numerical example is presented to illustrate the theoretical results.
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