Abstract:

In this thesis, input-output stability results for feedback systems are developed.  Robust Stability conditions are presented for nonlinear systems with nonlinear uncertainty defined by some function (with argument equal to the norm of the input) that bounds its output norm. A sufficient small gain theorem for a class of these systems is shown. Then it is also shown that, for the vector spaces (l_{\infty}, || · ||_{\infty}) and (l_2,|| · ||_2), the sufficient condition are also necessary with some additional assumptions on the systems. The application of those results may now be extended to classes of nonlinear systems that need not have their output norm bounded by a linear function of the input norm (as before).