In this paper, a nonlinear control scheme is proposed for synchronous generators in a multimachine power system to damp out low-frequency oscillations and enhance the transient stability. The proposed controller is designed recursively to adapt some unknown stability sensitive parameters of synchronous generators. These unknown parameters, estimated through the adaptation laws with the inclusion of the projection operator, are incorporated into the controller to ensure the stability of whole power system with the formulation of control Lyapunov functions (CLFs). The convergence of different physical properties of synchronous generators, such as relative speed, terminal voltage, and rotor angle, is ensured from the negative definiteness or semidefiniteness of the derivative of CLFs. The performance of the proposed controller is evaluated through simulation results on a two-area multimachine power system in terms of robustness to estimate the unknown parameters and maintain the steady-state operation of power systems under different operating conditions. Simulation results are compared with an existing nonlinear adaptive backstepping controller and a conventional power system stabilizer, which illustrate the effectiveness of the proposed control scheme over the existing controllers.