Filtrations in feedback synthesis: Part II – Input-output decoupling and disturbance decoupling

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.


The input-output decoupling problem and the disturbance decoupling problem are solved using the general feedback setting introduced in E. Delaleau and P. S. Pereira da Silva, Filtrations in feedback synthesis: Part I – Systems and feedbacks, Forum Math. 10 (1998) 147–174. Necessary and sufficient rank conditions are supplied, showing that endogenous state feedback is sufficiently general in order to solve these problems for generalized dynamics. The deffnitions of feedback of the first part of the paper are extended for considering the disturbed case, i.e., the case where dynamics are influenced by disturbances. For classical dynamics, most commonly considered in the literature, quasi-static state feedback is in fact rich enough for solving these problems. This kind of feedback, which is in between the static and the general dynamic feedback, does not require the integration of any differential equation.

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Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.