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The convergence of non-cooperative distributed power control in Gaussian interference channel is analysed in this study. Firstly, the existing distributed power control schemes are categorised as two types: gradient projection type and non-linear type, according to the iterative steps. A unified mathematical formulation is then provided for each type. The objective is extended from rate maximisation, which has been studied a lot in iterative water-filling game, to more general form of utility maximisation. Based on it, a set of sufficient conditions are derived for each type of the schemes, guaranteeing the uniqueness of the fixed point and the global convergence in a totally asynchronous manner. These convergence requirements can be interpreted as different degree of separation, according to the concrete form of utility function. To get insight into the derived convergence conditions, some numerical results are presented in the end.