Local-Global Double Algebras for Slow H" Adaptation: Part I-Inversion and Stability
نویسنده
چکیده
In this two-part paper, a common algebraic framework is introduced for the frozen-time analysis of stability and H"-optimization in slowly time-varying systems, based on the notion of a normed algebra on which local and global products are defined. Relations between local stability, local (near) optimality, lotal coprime factorization, and global versions of these properties are sought. The framework is valid for time-domain disturbances in 1". H"-behavior is related to 1" input-output behavior via the device of an approximate isometry between frequency and time-domain norms. Part I elaborates the double-algebra concept for Volterra operators which approximately commute with the shift. The main algebraic properties and norm inequalities are summarized. Local conditions for global invertibility are obtained. Clalssical frozen-time stability conditions are incorporated in relations between local and global spectra.
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