Abstract: In this paper, firstly we give the criterion for the absolute stability of the second canonical form for the control system, including .the equation of the longitudinal motions of a plane as a particular example. The corresponding result in [8],[9] is a particular example given in this paper. Secondly, we give the criteria for the absolute stability of the first canonical form in the usual case and in the critical case. Finally, we give some criteria for the absolute stability of the general form for the direct control system.All the results in this paper merely depend upon the relations between the parameters of the system itself to give an explicit algebraic discriminant.

Key words: chaotic time series, state space reconstruction, Legendre coordinates