Remarks on differential stability of nonlinear systems

Following up on earlier work (1993) the author discusses a generalization of the framework to encompass systems with inputs and outputs taking values on differential manifolds with no underlying linear structure. In this case, external disturbances are thought of as taking values in the group of diffeomorphism of these manifolds. The author deals with the special case where the input/output manifolds are Lie groups. The stability of a feedback interconnection relates to a geometric decomposition of the input-output manifold by the graphs of plant and controller