“…Furthermore, by defining and synthesizing (3) and (5), the dynamics of the whole system are described as: is regarded as a disturbance belonging to extended L 2 space due to the boundedness of x 5 . Thereby, there exists the following result.Proposition An adaptive controller, which renders the system (8) to be Lyapunov stable, states e , X to converge to the origin, and ensure L 2 attenuation for the interior and external disturbances, are designed as follows: …”