Etat de l'art sur le problème de synthèse multi-objectif H2/H∞, le retour d'état

Abstract

The goal of this article is to give a clear and comprehensive overview of the numerous studies concerning the multiobjective H 2 /H ∞ synthesis problem for continuous-time linear time-invariant systems. First, the more general problem as well as the possible variations and the associated assumptions are exposed. Then, the known analytical results lead naturally to define the multiobjective fixed-order synthesis problem. In this first part, only the state-feedback case is presented. Even for this simple case, no closed-form solution for the multiobjective synthesis problem can be found except in some particular cases. The approaches developed in the literature attempt therefore to get suboptimal solutions approximating the genuine optimal solution via more or less conservative convex relaxations. All the different frameworks (ranging from entropy maximization and game theory to Lyapunov theory and semidefinite programming) are dealt with. In almost every case, a very simple academic « by hand » numerical example is proposed.