Speaker: Radu Balan (CSCAMM, NWC)

Title: The non-commutative Wiener lemma and applications to distributed control of large-scale systems


The classic Wiener lemma states that the reciprocal of an absolutely Fourier series that does not vanish is also an absolutely convergent Fourier series. In this talk we present various non-commutative versions of the Wiener lemma particularly involving algebras of infinite matrices with certain off-diagonal decay. In a different context, an interesting question arises in connexion to optimal control of large-scale systems. Specifically one would like to obtain solutions to Liapunov and Riccati equations that are well-localized. In this framework, localization is equivalent to distributed implementation of optimal controllers. The talk will present some results on this topic.