ABSTRACT
The validity of the superposition principle induced by the linearity of the systems has permitted us to study separately systems reactions and prop- erties under zero initial conditions in a forced regime from the study of systems reactions and properties under zero input variables, i.e., in a free regime. This has simplified the study of many problems among which are the zero-state system equivalency and the zero-input system equivalency, see 5 for continuous-time systems. However, the zero-state systems equiv- alency and the zero-input system equivalency do not necessarily imply the system equivalence, which was discovered and proved by P. J. Antsaklis and A. N. Michel in [5, p. 171] for continuous-time systems.
