I/O equations for nonlinear systems and observation spaces

The authors study various types of input/output representations for nonlinear continuous-time systems. The algebraic and analytic I/O equations studied in previous work by the authors are generalized to integral and integro-differential equations, and an abstract notion is also considered. New results are given on generic observability, and these results are then applied to give conditions under which the minimal order of an equation equals the minimal possible dimension of a realization, just as with linear systems but in contrast to discrete-time nonlinear theory