Local-global double algebras for slow H∞ adaptation. II. Optimization of stable plants

For Pt.I see ibid., vol.36, no.2, p.130-42 (1991). The authors presently establish an explicit formula linking global and local sensitivity for systems with stable plants, in which local sensitivity is a Lipschitz-continuous function of data. Frequency-domain estimates of time-domain sensitivity norms, which become accurate as rates of time variation approach zero, are obtained. Notions of adaptive versus nonadaptive (robust) control are introduced. It is shown that adaptive control can achieve better sensitivity than optimal nonadaptive control. It is demonstrated that, in general, H^∞-optimal interpolants do not depend Lipschitz continuously on data. However, δ-suboptimal interpolants of the AAK central (maximal entropy) type are shown to satisfy a tractable Lipschitz condition