A generalized state space decomposition of nonlinear systems

Controllable and observable state space realizations of I/O nonlinear maps are considered, and their canonical decompositions are studied by means of generalized transformations. Notions of generalized transformations involving states and inputs, outputs and their derivatives are introduced which permit obtaining a certain kind of canonical form for the system. This can be viewed as a generalization of Morse's canonical form for linear systems, and can be shown to enjoy similar properties. The system obtained after applying the transformations necessary for displaying the canonical form is a generalized state-space realization.>