Impulsive behaviors of discrete and continuous time varying systems: A unified approach

A unified theory of continuous time impulsive behaviors (consisting of linear combinations of the Dirac distribution and its derivatives, generated by "inconsistent initial conditions") and of discrete time impulsive behaviors (consisting of backward solutions with finite support, generated by "inconsistent final consitions") is developed first in an analytic setting, then in an algebraic one; the latter is valid for possibly time varying systems. The effectiveness of the theory is illustrated through several examples.