%0 Journal Article %T Feedback Systems on a Reflexive Banach Space—Linearization %A Messaoudi Khelifa %J International Journal of Modern Nonlinear Theory and Application %P 34-50 %@ 2167-9487 %D 2020 %I Scientific Research Publishing %R 10.4236/ijmnta.2020.92003 %X 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 $\"\"$ . %K Nonlinear Feedback System %K Linearization %K Reflexive Banach Space %K Normality %K Lipschitz Continuity %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=100880