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Viewing input-output system equivalence from differential algebra. (English) Zbl 0806.93012
Summary: Input-output equivalence, transfer equivalence and transfer equivalence by compensation are considered for linear time-varying and nonlinear input-output systems. These systems are defined as modules in the linear and as differential field extensions in the nonlinear case. Generalizing the classical transfer matrix approach of the linear constant case, notions of transfer module in the linear and transfer extension in the nonlinear case are introduced. The notion of tangent linearized systems happens to be of great utility in this context. Conditions are obtained in terms of the differential output rank and subsystems of output- interaction. Real systems, important with respect to application, are introduced. The conditions given for equivalence by compensation are shown to be valid for real systems too.

93B25 Algebraic methods
12H05 Differential algebra
93C99 Model systems in control theory
93C10 Nonlinear systems in control theory