NECESSARY CONDITIONS FOR ROBUST STABILITY OF A CLASS OF NONLINEAR-SYSTEMS

Input-output stability results for feedback systems are developed. Rob ust stability conditions are presented for nonlinear systems with nonl inear uncertainty defined by some function (with argument equal to the norm of the input) that bounds its output norm. A sufficient small ga in theorem for a class of these systems is known. Here, necessary cond itions are presented for the vector space (l(infinity), parallel to.pa rallel to(infinity)). These results capture the conservatism of the sm all gain theorem as it is applied to systems that do not have linear g ain. The theory is also developed for the case of l(2) Signal norms, i ndicating some difficulties which make this case less natural than l(i nfinity). (C) 1998 Elsevier Science Ltd. All rights reserved.