Abstract
Compared with the case of linear systems, there seems to be some vagueness in the observability concept of nonlinear systems. That is, the “observability” of the nonlinear systems can not be defined without fixing the input. For such a reason, Brockett introduced the concept of distinguishability instead of observability in the study of bilinear systems. In this paper, the distinguishability for some generalized bilinear systems is defined and the concept of the indistinguishable manifold is introduced. Then it is shown that the tangent bundle of the indistinguishable manifold exhibits an invariant property very similar to the unobservable subspace of the linear systems. In practice, it will be almost impossible to calculate the one parameter group of the vector field, so it seems necessary to establish some feasible method for the observation. In this paper, the method which utilizes the higher order derivatives of the output is proposed. Then, for some class of systems, it is shown that if the system is distinguishable, it is distinguishable by differentiation.
