Abstract: A new adaptive controller-relay and proportional plus integral (P+I) combined controller based on Lyapunov's direct second method is derived and investigated. Some important problems encountered in the adaptive control systems is needed to solve such as nonlinear adaptive control systems; filtered input and output method to avoid the necessity of deterining the derivatives of the plant output; the transfer function of dimension difference problem between the model and the plant; combination of feedforward controller and adaptive controller; the stability of non-minimum phase adaptive control systems and appiied optimization design of adaptive controller parameters. The rear-time microprocessor application of this combined controller to the first and second order analog plants is also investigated using microcomputer IBM PC/XT and extended BASIC laugange. A generalized optimization program we developed is recommended.