Continuous-time H ∞ Almost Disturbance Decoupling

Abstract

We consider in this chapter the problem of H ∞ almost disturbance decoupling with measurement feedback and internal stability for continuous-time linear systems. Although in principle it is a special case of the general H ∞ control problem, i.e., the case that γ* = 0, the problem of almost disturbance decoupling has a vast history behind it, occupying a central part of classical as well as modern control theory. Several important problems, such as robust control, decentralized control, non-interactive control, model reference or tracking control, H 2 and H ∞ optimal control problems can all be recast into an almost disturbance decoupling problem. Roughly speaking, the basic almost disturbance decoupling problem is to find an output feedback control law such that in the closed-loop system the disturbances are quenched, say in an L p sense, up to any pre-specified degree of accuracy while maintaining internal stability. Such a problem was originally formulated by Willems ([136] and [137]) and labelled ADDPMS (the almost disturbance decoupling problem with measurement feedback and internal stability). In the case that, instead of a measurement feedback, a state feedback is used, the above problem is termed ADDPS (the almost disturbance decoupling problem with internal stability). The prefix H ∞ in the acronyms H ∞-ADDPMS and H ∞-ADDPS is used to specify that the degree of accuracy in disturbance quenching is measured in L 2-sense.