Nonlinear performance of a PI controlled missile: an explanation

Abstract

SUMMARYThe primary aim of this paper is to investigate the practical interest of the incremental norm approach for analysing (realistic) nonlinear dynamical systems. In this framework indeed, incremental stability, a stronger notion than L -gain stability, ensures suitable qualitative and quantitative properties. On the one hand, the qualitative properties essentially correspond to (steady-state) input/output properties, which are not necessarily obtained when ensuring only L -gain stability. On the other hand, it is possible to analyse quantitative robustness performance properties using the notion of (nonlinear) incremental performance, the latter being de"ned in the continuity of the (linear) H performance (i.e. through the use of a weighting function). As testing incremental properties is a di$cult problem, stronger, but computationally more attractive, notions are introduced, namely quadratic incremental stability and performance. Testing these properties reduces indeed to solving convex optimization problems over Linear Matrix Inequalities (LMIs). As an illustration, we consider a classical missile 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 stability and performance, the closed loop nonlinear missile is proved to meet desirable control speci"cations.

Convergent dynamics, a tribute to Boris Pavlovich Demidovich

“…Fromion et al established certain links between such incremental stability and Lyapunov stability of solutions [6]. They also introduced su cient conditions to check the Lipschitz continuity condition (the so-called quadratic incremental stability) [7], which are very close to the Demidovich conditions mentioned above. A Lyapunov approach unifying both state-space and input-to-output approaches to studying stability of solutions with respect to each other was developed by Angeli [1].…”

The global output regulation problem: An incremental stability approach

“…The purpose of the notions introduced above becomes clear from the following lemma, see (Demidovich, 1961;Fromion et al, 1999).…”

“…In this paper, we provide a global solution to the output regulation problem based on the so-called incremental stability property (Demidovich, 1961;Angeli, 2002;Fromion et al, 1999). Roughly speaking, every solution of a system with this property is globally asymptotically stable.…”

Design of Convergent Switched Systems

“…The property that all solutions of a system "forget" their initial conditions and converge to some steady-state solution has been addressed in a number of publications [8,39,32,20,41,22,10,11,13,2]. In this paper we continue the study originated in [33,31] on convergency of piece-wise affine (PWA) systems.…”