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This paper applies Kalman's procedure for the construction of Lur'e-type Lyapunov functions to a single-machine system with and without a velocity governor. The procedure uses the theorem of Popov on the absolute stability of nonlinear systems. The Lyapunov function so derived is used for estimating the region of asymptotic stability of the postfault system. The method is applicable to a single-machine system with any type of governor that admits of a representation by linear dynamics, the order being immaterial. Numerical examples are given.