Transformations and Representations of Nonlinear Systems

  • A. J. van der Schaft
Part of the Progress in Systems and Control Theory book series (PSCT, volume 2)


This paper deals with nonlinear systems described by sets of smooth algebraic and (higher-order) differential equations in the external variables (inputs and outputs), as well as auxiliary variables (states, driving variables). A general theorem for transforming such a system into a locally equivalent one, assuming constant rank conditions, is formulated. With the aid of this theorem it is shown how one can eliminate the auxiliary variables in the system description. Conversely, necessary and sufficient conditions for representing a system only involving inputs and outputs as a state space system are derived. Finally the techniques are applied to the construction of inverse systems.


Implicit Function Theorem Solution Point Constant Rank Inverse System State Space Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • A. J. van der Schaft
    • 1
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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