Filtrations in feedback synthesis: Part I – Systems and feedbacks

Emmanuel Delaleau 1  and Paulo Sérgio Pereira da Silva 2
  • 1 Laboratoire des signaux et systèmes, Université Paris XI – CNRS – Supélec, Plateau de Moulon, F-91192 Gif-sur-Yvette, France.
  • 2 Dep. Eng. Eletrônica, Escola Politécnica, Universidade de São Paulo, Av. Prof. Luciano Gualberto, travessa 3, no. 158, Cidade Universitária, São Paulo – SP Cep 05508-900, Brazil.


This paper presents an intrinsic differential algebraic framework for considering feedback in nonlinear control systems. In particular, filtrations of differential field extensions are shown to be useful for the definition of state feedback and the interpretation of two algorithms, namely the Structure Algorithm and the Dynamic Extension Algorithm, wellknown in the context of control theory. This difierential algebraic approach allows defining quasi-static state feedback.

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