The primary aim of this paper is to investigate the practical interest of t
he incremental norm approach for analysing (realistic) nonlinear dynamical
systems. In this framework indeed, incremental stability, a stronger notion
than L-2-gain stability, ensures suitable qualitative and quantitative pro
perties. On the one hand, the qualitative properties essentially correspond
to (steady-state) input/output properties, which are not necessarily obtai
ned when ensuring only L-2-gain stability. On the other hand, it is possibl
e to analyse quantitative robustness performance properties using the notio
n of(nonlinear) incremental performance, the latter being defined in the co
ntinuity of the (linear) H-infinity performance (i.e. through the use of a
weighting function). As testing incremental properties is a difficult probl
em, stronger, but computationally more attractive, notions are introduced,
namely quadratic incremental stability and performance. Testing these prope
rties reduces indeed to solving convex optimization problems over Linear Ma
trix Inequalities (LMIs). As an illustration, we consider a classical missi
le problem, which was already treated using several (linear and nonlinear)
approaches. We focus here on the analysis of the nonlinear behavior of this
PI. controlled missile: using the notions of quadratic incremental stabili
ty and performance, the closed loop nonlinear missile is proved to meet des
irable control specifications. Copyright (C) 1999 John Wiley & Sons, Ltd.