Local-global double algebras for slow H∞ adaptation

A common algebraic framework for the frozen-time analysis of stability and H^∞ optimization in slowly time-varying systems, which is based on the notion of an algebra with local and global products, is introduced. Relationships among local stability, local (near) optimality, local coprime factorization, and global versions of these properties are obtained. The framework is valid for time-domain disturbances in l^∞. H ^∞-behavior is related to I^∞-input-output behavior by means of an approximate isometry between frequency- and time-domain norms. It is shown that optimal H^∞ interpolants in general do not depend Lipschitz-continuously on the data. δ-suboptimal maximal entropy interpolants are employed instead, and their Lipschitz continuity is established