In order to study the electric network constraint relationship under the condition of voltage fluctuation, this paper establishes the analytic signal models for the voltage and current of the linear time-invariant loads with supply voltage fluctuation based on the Hilbert transform. Then, the linear time-invariant electric network topology constraints and element constraints represented by analytic signals are derived, which are the generalization of phasor method extended to the analysis and solution of the response characteristics of linear time-invariant electric networks under supply voltage fluctuation. The simulation experiment results show that the electric network constraint relationship based on the Hilbert transform is not only clear in physical meaning and concise in characterization, but also correct and easy to use when the supply voltage fluctuates. The relationship established in this paper can provide guidance for the analysis and calculation of the voltage-current relationship on the linear time-invariant loads under the condition of supply voltage fluctuations.