A Unification of System Equivalence Definitions.
STANFORD UNIV CALIF DEPT OF ELECTRICAL ENGINEERING
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The concept of system equivalence was introduced to generalize the notion of system similarity to nonstate-space models, i.e., to systems described by polynomial operators. The idea of equivalence is relatively natural given two descriptions of the same physical system by two different observers, one would like to assert whether these descriptions are the same from a coordinate-free point of view. In this paper, system equivalence is studied from both the polynomial and the state-space points of view. Previous definitions of system equivalence are connected together, and an alternative definition is proposed. This new approach is based on constructing complete information sets for a given differential system by expanding its usual inputoutput map. This idea generalizes the earlier concept of maximal-strict system equivalence.
- Theoretical Mathematics