STATE-SPACE REALIZATION OF NONLINEAR INPUT-OUTPUT DELTA DIFFERENTIAL EQUATIONS ON HOMOGENEOUS TIME SCALES

The paper studies the nonlinear control systems on time scales that serve as models of time and unify the continuous and discrete time. The realization problem for single-input single-output nonlinear delta differential systems is studied through the language of differential forms. Necessary and sufficient conditions are given for the existence of a state-space realization of the nonlinear input-output delta differential equation, i.e. a higher order delta differential equation relating the input, the output and a finite number of their delta-derivatives. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for obtaining an observable state-space description.