ABSTRACT
P. J. Antsaklis and A. N. Michel showed that the zero-state system equivalence and the zero-input system equivalence do not imply the system equivalence [8, p. 171]. They noted [8, p. 387] that di¤erent state-space realizations of the system transfer function matrix lead to the same zero-state system response, but the corresponding zero-input system response can be di¤erent. Their conclusions correspond to the real system environment and its history, which are the reasons to study the simultaneous in‡uence of arbitrary initial conditions and arbitrary inputs. This is essential for the analysis of the system behavior, of the system equivalence, of the system realization and the system minimal realization, and of many system dynamic properties (e.g., BIBO and L-stability under arbitrary initial conditions, total system stability, system tracking and system optimality). This led to Basic problem 42 (Subsection 3.2.2). Another, more speci…c, form follows.
