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.
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.