H ∞ Control: A Signature Condition Based Approach

This chapter is dedicated to a problem that undoubtedly dominated the Mathematical Control Theory during the last decade. Roughly speaking, the problem consists in finding a controller which simultaneously stabilizes and achieves disturbance attenuation under a prescribed tolerance level. In fact, the enormous attention paid to the problem above sketched can be explained by the necessity of providing appropriate solutions of the current generation of applications which have posed new kinds of control requirements. Among these the question of robustness is crucial. To be more specific, we have to say that, as in fact is well known, the fundamental requirement of feedback systems is to achieve stability and accomplish performance objectives not only for a single nominal model, but also for a set of models covering expected uncertainties about the model parameters and perturbations. Controllers which possesses this property are called ‘robust’. What was spectacular for the H∞-control theory was that this theory provided an elegant and complete solution of the robust control problem.