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4 - Stein Relations and Observability Range Spaces

Published online by Cambridge University Press:  09 December 2021

Joseph A. Ball
Affiliation:
Virginia Tech
Vladimir Bolotnikov
Affiliation:
College of William and Mary, Virginia
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Summary

Chapter 4 is concerned with the state/output part of a noncommutative linear system and the range of the associated observability operator. Specifically, (i) observability operators having range landing inside of a given weighted Hardy–Fock space are characterized by the existence of a solution to certain Linear Matrix Inequality (Linear Operator Inequality in general) called a Stein inequality, (ii) conversely, subspaces of a given weighted Hardy–Fock space arising as the range of a contractive observability operator are characterized as contractively included backward-shift-invariant subspaces of the ambient Hardy–Fock space having some additional natural structural properties.

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Publisher: Cambridge University Press
Print publication year: 2021

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