This paper describes an adaptive bilinear control method for the design of a single-machine infinite-bus (SMIB) power system stabilizer (PSS). The novelty of this approach is that the inherent nonlinearities of the underlying system are incorporated into the design of the control law in a simple and practical manner. An adaptive bilinear PSS is proposed, and a theoretical proof of convergence of the adaptive bilinear control algorithm is given. The significance of the adaptive bilinear PSS lies in that : (i) its nonlinear nature accounts for dynamic changes of the system due to the system’s inherent nonlinearities; and (ii) its adaptive feature accommodates changes in the system parameters and/or configuration.