The coefficient matrix of the state equations is essential for stability analysis of the governor-turbine hydraulic (GTH) system by the state space method. With plant layout becoming more and more complicated, it is important to derive the state matrix quickly and accurately. Based on the stability analysis theory of the GTH system, this paper investigates regular features of the state equations that describe small fluctuations in the state variables of the system. The equations for unsteady flow in the pipeline system are conveniently given by using graph theory. By specifying the order of the state variables and using matrix transformation, an innovative method for solving the coefficient matrix of the state equations is established, and the stable region of the system can be given with the eigenvalue method. The proposed method is used to analyze the stability of a practical hydropower station during small fluctuation, which is also verified in the hydraulic transient model of hydropower system on the basis of characteristics method. (C) 2016 Elsevier Ltd. All rights reserved.