On dynamic state feedback in nonlinear control

This paper presents a review of present day results on dynamic state feedback in nonlinear control systems. Some basic control problems involving dynamic state feedbacks are the dynamic input-output decoupling problem and the dynamic disturbance decoupling problem. In the dynamic input-output decoupling problem one tries to design a compensator for the system so that the closed loop system is input-output decoupled. The dynamic disturbance decoupling problem requires one to construct, if possible, a dynamic feedback such that the output y is independent from the (unknown) disturbance independent of the choice of the new input. The (local) solvability of both problems is analyzed via the use of a structural algorithm, which is a generalization of a similar structure algorithm for linear systems. Alternatively, the solvability question can be studied in a more simple manner by relating the system with its linearization about a given equilibrium. Under generic conditions, the solvability of the dynamic input-output decoupling problem and the dynamic disturbance decoupling problem for the nonlinear system C is equivalent to the solvability of the same problems for the linearized system