Nonlinear performance of a PI controlled missile: An explanation

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.