In this paper, a robust adaptive excitation control scheme is proposed for synchronous generators in multimachine power systems. The controller is designed to provide robustness against parametric uncertainties and external disturbances while enhancing the transient stability of multimachine power systems. The dynamics of synchronous generators and excitation systems are used to design the controller. The parametric uncertainties are incorporated by considering the parameters of synchronous generators and exciters, which degrades the stability margin, as totally unknown. The unknown parameters are estimated through adaptation laws and external disturbances are bounded to guarantee the overall stability of multimachine power systems. The stability of multimachine power systems is analyzed using control Lyapunov functions (CLFs) and proved through the negative semi-definiteness of the derivative of CLFs. The performance of the proposed control scheme is evaluated on an IEEE standard 10 Machine 39-bus New England test system and compared with an existing adaptive excitation controller.