The novel concepts and definitions of derivativeand bracket for nonlinear differential algebraic system (NDAS)are introduced, and some related revised results that are similarto the classic differential geometric theory are given. The normalforms of NDAS model are obtained by multi-input multi-output(MIMO) feedback linearization technique. The control expressionsderived are based on the linear system theory and the requirementsof tracking targets when the relative degree of the systemis less than the dimension of the system and the special designatedconditions are satisfied. The parametric adaptive controller is obtainedfor the multimachine power systems with nonlinear loadsand undetermined or unknown parameters by the Lyapunov stabilitytheory and method.