The design of an adaptive controller and stability analysis of the corresponding closed loop system are discussed for a class of SISO systems based on the characteristic model method. The obtained characteristic model is a second-order slow time-varying linear system with a compress mapping function for the system modeling error. The pole placement method is used to design the controller, and sufficient conditions for the stability of the closed loop system are obtained based on the robust control theory of slow time-varying systems with perturbations. The effectiveness of the proposed method is illustrated by two numerical examples. The design of an adaptive controller and stability analysis of the corresponding closed loop system are discussed for a class of SISO systems based on the characteristic model method. The obtained characteristic model is a second-order slow time-varying linear system with a compress mapping function for the system modeling error. The pole placement method is used to design the controller, and sufficient conditions for the stability of the closed loop system are obtained based on the robust control theory of slow time-varying systems with perturbations. The effectiveness of the proposed method is illustrated by two numerical examples.