Realizations of Nonlinear Control Systems on Time Scales

Nonlinear partially defined systems on an arbitrary unbounded time scale are studied. They include continuous-time and discrete-time systems. The main problem is to find necessary and sufficient conditions for an abstract input/output map to have a realization as a nonlinear system of a specific class on the time scale. The obtained results extend criteria of realizability of continuous-time polynomial systems. A simple construction of a realization is provided.