Feedback Controls for Finite Time or Asymptotic Compensation in Lumped Disturbed Systems

In this paper, we study the possibility of finite time or asymptotic compensation of disturbances f,
for a class of linear lumped systems

g.png

augmented with the output equation

fg.png

using directly feedback controls u = K f, where K is a linear operator. We give appropriate
definitions and characterization results of this notion, called K-remediability. We also examine the
relationship with the remediability as studied in previous works. Illustrative examples are presented
and various situations are considered. The relation u = K f includes the usual form u = K yf ,
where yf is the term corresponding, in the expression of the observation y, to the disturbance f. In
the linear case, yf may be deduced easily from the observation y, even if f is not known.