In this paper parameter space and Lebesgue measurement are introduced into analysis of nonlinear systems. Structural observability rank condition is defined and together with the distinguishabililty the structural observability criterions of nonlinear systems are obtained. It proves that when the parameters are not identifiable the solutions with the same time but different parameters are also indistinguishable. Differential geometry and algebraic methods are used to investigate the observability problem, and it is proved that there are some relations between these two methods. Finally, examples are used to illustrate applications of the structural observability criterions.

In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix) of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.