Understanding the stability inherent in limit cycle walking with constraint on impact posture without numerical integral is one of the fundamental goals in the area of robotic legged locomotion. The two major methods to analyze the stability of generated dynamic gaits have ever been proposed. One is the method for deriving the transition function of the state error using linearization of motion, and the other is that for describing the convergence of the kinetic energy based on mechanical energy balance. In both methods, however, numerical integral was necessary. In this paper, we theoretically show that it is possible to achieve stability analysis without numerical integral by integrating the two methods. First, we analytically derive the transition functions of the state error without including unknown variables for a 1-DOF semipassive walker and evaluate the solution accuracy through numerical simulations. Second, we consider a 2-DOF underactuated walker and show that the stability of the generated level gait can be analyzed in the same manner as the 1-DOF walker.