The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see
[1] [2] [3]. We then consider a linear FS
, and prove that, if
;
, with
the respective solutions of FS’s [A,B] and
corresponding to the given (u,v) in
. There exists,
, positive real constants such that,
. These results are the subject of theorems 3.1,
... , 3.3. The proofs of these theorems are based on our lemmas 3.2,
... , 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator
I+BA and
. The results obtained and demonstrated along this document, present an extension in general Banach space of those in
[4] on a Hilbert space
H and those in
[5] on a extended Hilbert space
.