Transfer Equivalence and Realization of Nonlinear Input-Output Delta-Differential Equations on Homogeneous Time Scales

Nonlinear control systems on homogeneous time scales are studied. First the concepts of reduction and irreducibility are extended to higher order delta-differential input-output equations. Subsequently, a definition of system equivalence is introduced which generalizes the notion of transfer equivalence in the linear case. Finally, the necessary and sufficient conditions are given for the existence of a state-space realization of a nonlinear input-output delta-differential equation.